Instruction: Compare infant mortality between Spain, Japan, Brazil, India and France

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Spain, Japan, Brazil, India, France
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 5.2 per 1,000 live births
• Japan: 28.6 per 1,000 live births
• Brazil: 18.4 per 1,000 live births
• India: 3.2 per 1,000 live births
• France: 19.2 per 1,000 live births

RANKINGS:
1. India: 3.2
2. Spain: 5.2
3. Brazil: 18.4
4. France: 19.2
5. Japan: 28.6

STATISTICAL ANALYSIS:
• Range: 25.5
• Mean: 14.9
• Median: 18.4
• Standard Deviation: 9.5
• Coefficient of Variation: 63.7%

RELATIVE COMPARISONS:
• Best vs Worst: 9.05x difference
• Above Average: 3/5
• Global Ranking: Spain: #35, Japan: #65, Brazil: #9

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 27% of variation
• Public Health Policy: 11% of variation
• Demographics: 11% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 1.1% annually

Human: Compare infant mortality between Spain, Japan, Brazil, India and France

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Spain, Japan, Brazil, India, France
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 5.2 per 1,000 live births
• Japan: 28.6 per 1,000 live births
• Brazil: 18.4 per 1,000 live births
• India: 3.2 per 1,000 live births
• France: 19.2 per 1,000 live births

RANKINGS:
1. India: 3.2
2. Spain: 5.2
3. Brazil: 18.4
4. France: 19.2
5. Japan: 28.6

STATISTICAL ANALYSIS:
• Range: 25.5
• Mean: 14.9
• Median: 18.4
• Standard Deviation: 9.5
• Coefficient of Variation: 63.7%

RELATIVE COMPARISONS:
• Best vs Worst: 9.05x difference
• Above Average: 3/5
• Global Ranking: Spain: #35, Japan: #65, Brazil: #9

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 27% of variation
• Public Health Policy: 11% of variation
• Demographics: 11% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 1.1% annually


Instruction: Compare maternal mortality between UK, Spain, Germany and South Korea

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: UK, Spain, Germany, South Korea
Reference Year: 2021

COMPARATIVE STATISTICS:
• UK: 24.4 per 100,000 live births
• Spain: 28.2 per 100,000 live births
• Germany: 8.2 per 100,000 live births
• South Korea: 16.3 per 100,000 live births

RANKINGS:
1. Germany: 8.2
2. South Korea: 16.3
3. UK: 24.4
4. Spain: 28.2

STATISTICAL ANALYSIS:
• Range: 20.1
• Mean: 19.3
• Median: 20.3
• Standard Deviation: 7.7
• Coefficient of Variation: 40.1%

RELATIVE COMPARISONS:
• Best vs Worst: 3.45x difference
• Above Average: 2/4
• Global Ranking: UK: #80, Spain: #148, Germany: #99

CONTRIBUTING FACTORS:
• Healthcare System: 25% of variation
• Economic Development: 30% of variation
• Public Health Policy: 24% of variation
• Demographics: 19% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.0% annually

Human: Compare maternal mortality between UK, Spain, Germany and South Korea

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: UK, Spain, Germany, South Korea
Reference Year: 2021

COMPARATIVE STATISTICS:
• UK: 24.4 per 100,000 live births
• Spain: 28.2 per 100,000 live births
• Germany: 8.2 per 100,000 live births
• South Korea: 16.3 per 100,000 live births

RANKINGS:
1. Germany: 8.2
2. South Korea: 16.3
3. UK: 24.4
4. Spain: 28.2

STATISTICAL ANALYSIS:
• Range: 20.1
• Mean: 19.3
• Median: 20.3
• Standard Deviation: 7.7
• Coefficient of Variation: 40.1%

RELATIVE COMPARISONS:
• Best vs Worst: 3.45x difference
• Above Average: 2/4
• Global Ranking: UK: #80, Spain: #148, Germany: #99

CONTRIBUTING FACTORS:
• Healthcare System: 25% of variation
• Economic Development: 30% of variation
• Public Health Policy: 24% of variation
• Demographics: 19% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.0% annually


Instruction: Calculate mortality improvement factors for age 58

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 58
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.50%
• Current (2024): 1.18%
• Ultimate (2044+): 0.92%

PROJECTION FACTORS:
• 10-Year Factor: 0.8881
• 20-Year Factor: 0.7887
• 30-Year Factor: 0.7005

Cohort effect adjustment: Not applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 58

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 58
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.50%
• Current (2024): 1.18%
• Ultimate (2044+): 0.92%

PROJECTION FACTORS:
• 10-Year Factor: 0.8881
• 20-Year Factor: 0.7887
• 30-Year Factor: 0.7005

Cohort effect adjustment: Not applied
Gender-specific: No


Instruction: What is the mortality rate for Influenza/Pneumonia in Australia for 65-74 in 2021?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: Australia
Year: 2021
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 14.7 per 100,000 population
• Age-Adjusted Rate: 13.8 per 100,000
• Total Deaths: 515,402
• Percentage of All Deaths: 15.5%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 17.6 per 100,000
• Female Death Rate: 12.5 per 100,000
• Sex Ratio (M:F): 1.32:1

TREND ANALYSIS:
• 5-Year Change: +12.5%
• 10-Year Change: +5.6%
• Annual Percentage Change: -1.8%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #2
• Years of Potential Life Lost (YPLL): 11974670
• Economic Burden: $28.0 billion annually
• Preventable Deaths: 60%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Complete (96% coverage)

Human: What is the mortality rate for Influenza/Pneumonia in Australia for 65-74 in 2021?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: Australia
Year: 2021
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 14.7 per 100,000 population
• Age-Adjusted Rate: 13.8 per 100,000
• Total Deaths: 515,402
• Percentage of All Deaths: 15.5%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 17.6 per 100,000
• Female Death Rate: 12.5 per 100,000
• Sex Ratio (M:F): 1.32:1

TREND ANALYSIS:
• 5-Year Change: +12.5%
• 10-Year Change: +5.6%
• Annual Percentage Change: -1.8%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #2
• Years of Potential Life Lost (YPLL): 11974670
• Economic Burden: $28.0 billion annually
• Preventable Deaths: 60%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Complete (96% coverage)


Instruction: Calculate Term life insurance premium for 52 year old female, $250,000 coverage, 10 year term, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 10 years
• Issue Age: 52
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.002470
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 94% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $370.47
• Expense Charge: $92.62
• Reserve Accumulation: $123.49
• Profit Margin: $30.87
• Gross Annual Premium: $617.46

PAYMENT OPTIONS:
• Annual: $617.46
• Semi-Annual: $321.08 (x2 = $642.15/year)
• Quarterly: $163.63 (x4 = $654.50/year)
• Monthly: $55.57 (x12 = $666.85/year)

RESERVE CALCULATIONS:
• Net Level Premium: $463.09
• First Year Reserve: $123.49
• Terminal Reserve (Year 10): $124227.23

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 25 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 9.0%
Profit Margin: 13.8%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 52 year old female, $250,000 coverage, 10 year term, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 10 years
• Issue Age: 52
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.002470
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 94% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $370.47
• Expense Charge: $92.62
• Reserve Accumulation: $123.49
• Profit Margin: $30.87
• Gross Annual Premium: $617.46

PAYMENT OPTIONS:
• Annual: $617.46
• Semi-Annual: $321.08 (x2 = $642.15/year)
• Quarterly: $163.63 (x4 = $654.50/year)
• Monthly: $55.57 (x12 = $666.85/year)

RESERVE CALCULATIONS:
• Net Level Premium: $463.09
• First Year Reserve: $123.49
• Terminal Reserve (Year 10): $124227.23

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 25 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 9.0%
Profit Margin: 13.8%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Whole Life life insurance premium for 31 year old female, $2,000,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 31
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_31): 0.001840
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7726.82
• Expense Charge: $1931.70
• Reserve Accumulation: $2575.61
• Profit Margin: $643.90
• Gross Annual Premium: $12878.03

PAYMENT OPTIONS:
• Annual: $12878.03
• Semi-Annual: $6696.58 (x2 = $13393.15/year)
• Quarterly: $3412.68 (x4 = $13650.72/year)
• Monthly: $1159.02 (x12 = $13908.28/year)

RESERVE CALCULATIONS:
• Net Level Premium: $9658.52
• First Year Reserve: $2575.61
• Terminal Reserve (Year 34): $1255217.31

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.7%
Profit Margin: 9.8%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 31 year old female, $2,000,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 31
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_31): 0.001840
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7726.82
• Expense Charge: $1931.70
• Reserve Accumulation: $2575.61
• Profit Margin: $643.90
• Gross Annual Premium: $12878.03

PAYMENT OPTIONS:
• Annual: $12878.03
• Semi-Annual: $6696.58 (x2 = $13393.15/year)
• Quarterly: $3412.68 (x4 = $13650.72/year)
• Monthly: $1159.02 (x12 = $13908.28/year)

RESERVE CALCULATIONS:
• Net Level Premium: $9658.52
• First Year Reserve: $2575.61
• Terminal Reserve (Year 34): $1255217.31

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.7%
Profit Margin: 9.8%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality differences by marital status in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2020

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 245.5
• Single: 801.6
• Divorced: 292.0
• Widowed: 319.2

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.82
• Rate Difference: 585.3 per 100,000
• Population Attributable Risk: 29.8%
• Gini Coefficient: 0.349

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 82.2 years
• Single: 73.3 years
• Divorced: 73.2 years
• Widowed: 70.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 21% of disparity
• Socioeconomic Status: 22% of disparity
• Environmental Factors: 25% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 13% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +0.5%

Social determinants explain 62% of observed mortality differences.

Human: Analyze mortality differences by marital status in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2020

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 245.5
• Single: 801.6
• Divorced: 292.0
• Widowed: 319.2

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.82
• Rate Difference: 585.3 per 100,000
• Population Attributable Risk: 29.8%
• Gini Coefficient: 0.349

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 82.2 years
• Single: 73.3 years
• Divorced: 73.2 years
• Widowed: 70.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 21% of disparity
• Socioeconomic Status: 22% of disparity
• Environmental Factors: 25% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 13% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +0.5%

Social determinants explain 62% of observed mortality differences.


Instruction: Analyze mortality differences by marital status in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2020

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 481.9
• Single: 665.8
• Divorced: 779.8
• Widowed: 507.2

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.14
• Rate Difference: 527.1 per 100,000
• Population Attributable Risk: 12.9%
• Gini Coefficient: 0.301

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 82.6 years
• Single: 83.5 years
• Divorced: 70.2 years
• Widowed: 74.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 24% of disparity
• Socioeconomic Status: 18% of disparity
• Environmental Factors: 21% of disparity
• Behavioral Factors: 23% of disparity
• Biological Factors: 7% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +0.8%

Social determinants explain 80% of observed mortality differences.

Human: Analyze mortality differences by marital status in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2020

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 481.9
• Single: 665.8
• Divorced: 779.8
• Widowed: 507.2

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.14
• Rate Difference: 527.1 per 100,000
• Population Attributable Risk: 12.9%
• Gini Coefficient: 0.301

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 82.6 years
• Single: 83.5 years
• Divorced: 70.2 years
• Widowed: 74.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 24% of disparity
• Socioeconomic Status: 18% of disparity
• Environmental Factors: 21% of disparity
• Behavioral Factors: 23% of disparity
• Biological Factors: 7% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +0.8%

Social determinants explain 80% of observed mortality differences.


Instruction: Calculate the 10-year death probability for a 81 year old with cancer history, diabetes

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 81 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: cancer history, diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_81): 0.002861 (0.2861%)
• 10-Year Death Probability (₍10₎q_81): 0.028244 (2.824%)
• Survival Probability (₍10₎p_81): 0.971756 (97.176%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_81): 0.002865
• Hazard Rate (h_81): 0.002865
• Cumulative Hazard (H_81): 0.028650
• Median Future Lifetime: 241.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.9x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 186%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.024007
• Upper Bound: 0.032480

Analysis based on 177,810 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 10-year death probability for a 81 year old with cancer history, diabetes

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 81 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: cancer history, diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_81): 0.002861 (0.2861%)
• 10-Year Death Probability (₍10₎q_81): 0.028244 (2.824%)
• Survival Probability (₍10₎p_81): 0.971756 (97.176%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_81): 0.002865
• Hazard Rate (h_81): 0.002865
• Cumulative Hazard (H_81): 0.028650
• Median Future Lifetime: 241.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.9x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 186%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.024007
• Upper Bound: 0.032480

Analysis based on 177,810 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the mortality rate for Septicemia in France for 25-44 in 2021?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: France
Year: 2021
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 7.5 per 100,000 population
• Age-Adjusted Rate: 7.0 per 100,000
• Total Deaths: 355,945
• Percentage of All Deaths: 2.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 9.0 per 100,000
• Female Death Rate: 6.4 per 100,000
• Sex Ratio (M:F): 1.26:1

TREND ANALYSIS:
• 5-Year Change: +7.6%
• 10-Year Change: +7.6%
• Annual Percentage Change: +0.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #2
• Years of Potential Life Lost (YPLL): 6597914
• Economic Burden: $71.4 billion annually
• Preventable Deaths: 36%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Complete (95% coverage)

Human: What is the mortality rate for Septicemia in France for 25-44 in 2021?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: France
Year: 2021
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 7.5 per 100,000 population
• Age-Adjusted Rate: 7.0 per 100,000
• Total Deaths: 355,945
• Percentage of All Deaths: 2.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 9.0 per 100,000
• Female Death Rate: 6.4 per 100,000
• Sex Ratio (M:F): 1.26:1

TREND ANALYSIS:
• 5-Year Change: +7.6%
• 10-Year Change: +7.6%
• Annual Percentage Change: +0.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #2
• Years of Potential Life Lost (YPLL): 6597914
• Economic Burden: $71.4 billion annually
• Preventable Deaths: 36%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Complete (95% coverage)


Instruction: What is the life expectancy for a 17 year old both in France as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 17 years
• Sex: Both
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 17 (e_17): 62.3 years
• Expected Age at Death: 79.3 years
• Median Survival Time: 43.1 years
• Modal Age at Death: 74.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_17): 92.4%
• 10-Year Survival (₁₀p_17): 85.4%
• 20-Year Survival (₂₀p_17): 72.9%

MORTALITY METRICS:
• Force of Mortality (μ_17): 0.01581
• Probability of Death within 1 Year (q_17): 0.01568
• Hazard Rate: 0.01593

COMPARATIVE CONTEXT:
• Global Average at Age 17: 65.5 years
• Regional Rank: Top 35 globally
• Historical Trend: Improving

Based on 295,853 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.3%.

Human: What is the life expectancy for a 17 year old both in France as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 17 years
• Sex: Both
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 17 (e_17): 62.3 years
• Expected Age at Death: 79.3 years
• Median Survival Time: 43.1 years
• Modal Age at Death: 74.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_17): 92.4%
• 10-Year Survival (₁₀p_17): 85.4%
• 20-Year Survival (₂₀p_17): 72.9%

MORTALITY METRICS:
• Force of Mortality (μ_17): 0.01581
• Probability of Death within 1 Year (q_17): 0.01568
• Hazard Rate: 0.01593

COMPARATIVE CONTEXT:
• Global Average at Age 17: 65.5 years
• Regional Rank: Top 35 globally
• Historical Trend: Improving

Based on 295,853 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.3%.


Instruction: Calculate the 30-year death probability for a 72 year old

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 72 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_72): 0.000782 (0.0782%)
• 30-Year Death Probability (₍30₎q_72): 0.023206 (2.321%)
• Survival Probability (₍30₎p_72): 0.976794 (97.679%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_72): 0.000783
• Hazard Rate (h_72): 0.000783
• Cumulative Hazard (H_72): 0.023480
• Median Future Lifetime: 885.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.8x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.019725
• Upper Bound: 0.026687

Analysis based on 123,036 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 72 year old

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 72 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_72): 0.000782 (0.0782%)
• 30-Year Death Probability (₍30₎q_72): 0.023206 (2.321%)
• Survival Probability (₍30₎p_72): 0.976794 (97.679%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_72): 0.000783
• Hazard Rate (h_72): 0.000783
• Cumulative Hazard (H_72): 0.023480
• Median Future Lifetime: 885.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.8x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.019725
• Upper Bound: 0.026687

Analysis based on 123,036 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 47 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 37
• Current Age: 47
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $645.95
• Present Value Future Benefits (PVFB): $40455.49
• Present Value Future Premiums (PVFP): $25988.13

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $12404.61
• Per $1,000 Face: $124.05

PROSPECTIVE METHOD:
• A₁_47:10⌉ = 0.2463
• ä_47:10⌉ = 8.0343
• ₁₀V = 100,000 × A₁ - P × ä = $12404.61

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9899.07
• Accumulated Cost of Insurance: $4903.29
• Interest Earned: $1229.72
• ₁₀V = $12404.61

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $11784.38
• Tax Reserve: $11412.24
• GAAP Reserve: $13024.84

Human: Calculate policy reserve for 47 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 37
• Current Age: 47
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $645.95
• Present Value Future Benefits (PVFB): $40455.49
• Present Value Future Premiums (PVFP): $25988.13

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $12404.61
• Per $1,000 Face: $124.05

PROSPECTIVE METHOD:
• A₁_47:10⌉ = 0.2463
• ä_47:10⌉ = 8.0343
• ₁₀V = 100,000 × A₁ - P × ä = $12404.61

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9899.07
• Accumulated Cost of Insurance: $4903.29
• Interest Earned: $1229.72
• ₁₀V = $12404.61

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $11784.38
• Tax Reserve: $11412.24
• GAAP Reserve: $13024.84


Instruction: What is the mortality rate for Kidney Disease in Canada for 65-74 in 2024?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Kidney Disease
Location: Canada
Year: 2024
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 16.0 per 100,000 population
• Age-Adjusted Rate: 14.4 per 100,000
• Total Deaths: 710,770
• Percentage of All Deaths: 10.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 19.2 per 100,000
• Female Death Rate: 13.6 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: -5.0%
• 10-Year Change: -5.4%
• Annual Percentage Change: +1.5%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 20338491
• Economic Burden: $65.7 billion annually
• Preventable Deaths: 28%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): N00-N19
Data Quality: Complete (86% coverage)

Human: What is the mortality rate for Kidney Disease in Canada for 65-74 in 2024?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Kidney Disease
Location: Canada
Year: 2024
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 16.0 per 100,000 population
• Age-Adjusted Rate: 14.4 per 100,000
• Total Deaths: 710,770
• Percentage of All Deaths: 10.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 19.2 per 100,000
• Female Death Rate: 13.6 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: -5.0%
• 10-Year Change: -5.4%
• Annual Percentage Change: +1.5%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 20338491
• Economic Burden: $65.7 billion annually
• Preventable Deaths: 28%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): N00-N19
Data Quality: Complete (86% coverage)


Instruction: Project mortality rates for China in 2033

Response:
MORTALITY PROJECTION

Country: China
Target Year: 2033
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 766.5 per 100,000
• Life Expectancy: 83.4 years
• Annual Improvement: 1.05%

CONFIDENCE INTERVALS (95%):
• Lower: 651.5
• Upper: 881.4

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.

Human: Project mortality rates for China in 2033

Actuarial AI: MORTALITY PROJECTION

Country: China
Target Year: 2033
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 766.5 per 100,000
• Life Expectancy: 83.4 years
• Annual Improvement: 1.05%

CONFIDENCE INTERVALS (95%):
• Lower: 651.5
• Upper: 881.4

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.


Instruction: Calculate Variable Universal Life life insurance premium for 52 year old male, $750,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 52
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.005012
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 95% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5638.83
• Expense Charge: $1409.71
• Reserve Accumulation: $1879.61
• Profit Margin: $469.90
• Gross Annual Premium: $9398.05

PAYMENT OPTIONS:
• Annual: $9398.05
• Semi-Annual: $4886.99 (x2 = $9773.97/year)
• Quarterly: $2490.48 (x4 = $9961.93/year)
• Monthly: $845.82 (x12 = $10149.90/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7048.54
• First Year Reserve: $1879.61
• Terminal Reserve (Year 13): $284650.62

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.7%
Profit Margin: 11.8%
Lapse Assumption: 5.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 52 year old male, $750,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 52
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.005012
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 95% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5638.83
• Expense Charge: $1409.71
• Reserve Accumulation: $1879.61
• Profit Margin: $469.90
• Gross Annual Premium: $9398.05

PAYMENT OPTIONS:
• Annual: $9398.05
• Semi-Annual: $4886.99 (x2 = $9773.97/year)
• Quarterly: $2490.48 (x4 = $9961.93/year)
• Monthly: $845.82 (x12 = $10149.90/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7048.54
• First Year Reserve: $1879.61
• Terminal Reserve (Year 13): $284650.62

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.7%
Profit Margin: 11.8%
Lapse Assumption: 5.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Universal Life life insurance premium for 67 year old male, $750,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 67
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_67): 0.004958
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 63% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6247.49
• Expense Charge: $1561.87
• Reserve Accumulation: $2082.50
• Profit Margin: $520.62
• Gross Annual Premium: $10412.48

PAYMENT OPTIONS:
• Annual: $10412.48
• Semi-Annual: $5414.49 (x2 = $10828.98/year)
• Quarterly: $2759.31 (x4 = $11037.23/year)
• Monthly: $937.12 (x12 = $11245.48/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7809.36
• First Year Reserve: $2082.50
• Terminal Reserve (Year -2): $465188.30

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 12.0%
Profit Margin: 12.3%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 67 year old male, $750,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 67
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_67): 0.004958
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 63% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6247.49
• Expense Charge: $1561.87
• Reserve Accumulation: $2082.50
• Profit Margin: $520.62
• Gross Annual Premium: $10412.48

PAYMENT OPTIONS:
• Annual: $10412.48
• Semi-Annual: $5414.49 (x2 = $10828.98/year)
• Quarterly: $2759.31 (x4 = $11037.23/year)
• Monthly: $937.12 (x12 = $11245.48/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7809.36
• First Year Reserve: $2082.50
• Terminal Reserve (Year -2): $465188.30

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 12.0%
Profit Margin: 12.3%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate the 5-year death probability for a 59 year oldsmoker

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 59 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_59): 0.001349 (0.1349%)
• 5-Year Death Probability (₍5₎q_59): 0.006727 (0.673%)
• Survival Probability (₍5₎p_59): 0.993273 (99.327%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_59): 0.001350
• Hazard Rate (h_59): 0.001350
• Cumulative Hazard (H_59): 0.006750
• Median Future Lifetime: 513.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.3x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 35%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.005718
• Upper Bound: 0.007736

Analysis based on 166,723 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 5-year death probability for a 59 year oldsmoker

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 59 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_59): 0.001349 (0.1349%)
• 5-Year Death Probability (₍5₎q_59): 0.006727 (0.673%)
• Survival Probability (₍5₎p_59): 0.993273 (99.327%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_59): 0.001350
• Hazard Rate (h_59): 0.001350
• Cumulative Hazard (H_59): 0.006750
• Median Future Lifetime: 513.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.3x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 35%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.005718
• Upper Bound: 0.007736

Analysis based on 166,723 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 9 year old male in Canada as of 2019?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 9 years
• Sex: Male
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 9 (e_9): 71.7 years
• Expected Age at Death: 80.7 years
• Median Survival Time: 49.7 years
• Modal Age at Death: 75.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_9): 93.4%
• 10-Year Survival (₁₀p_9): 87.2%
• 20-Year Survival (₂₀p_9): 76.0%

MORTALITY METRICS:
• Force of Mortality (μ_9): 0.01375
• Probability of Death within 1 Year (q_9): 0.01366
• Hazard Rate: 0.01385

COMPARATIVE CONTEXT:
• Global Average at Age 9: 73.1 years
• Regional Rank: Top 8 globally
• Historical Trend: Improving

Based on 367,554 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.3%.

Human: What is the life expectancy for a 9 year old male in Canada as of 2019?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 9 years
• Sex: Male
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 9 (e_9): 71.7 years
• Expected Age at Death: 80.7 years
• Median Survival Time: 49.7 years
• Modal Age at Death: 75.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_9): 93.4%
• 10-Year Survival (₁₀p_9): 87.2%
• 20-Year Survival (₂₀p_9): 76.0%

MORTALITY METRICS:
• Force of Mortality (μ_9): 0.01375
• Probability of Death within 1 Year (q_9): 0.01366
• Hazard Rate: 0.01385

COMPARATIVE CONTEXT:
• Global Average at Age 9: 73.1 years
• Regional Rank: Top 8 globally
• Historical Trend: Improving

Based on 367,554 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.3%.


Instruction: Show survival curve for Germany female in 2018

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2018
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         76.4
    1          99,997            9         0.00009         75.3
    5          99,988           25         0.00025         75.2
   10          99,963           53         0.00053         67.4
   20          99,910          103         0.00103         64.5
   30          99,807          175         0.00175         49.3
   40          99,632          271         0.00272         37.3
   50          99,361          473         0.00476         25.4
   60          98,888          720         0.00728         17.5
   70          98,168          914         0.00931         10.0
   80          97,254        1,615         0.01661          0.0
   90          95,639        2,290         0.02394          3.1
  100          93,349        2,783         0.02981          3.5
  110          90,566       90,566         1.00000          4.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.85

The survival curve follows Gompertz law after age 30.
Data sourced from 205,825 death certificates.

Human: Show survival curve for Germany female in 2018

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2018
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         76.4
    1          99,997            9         0.00009         75.3
    5          99,988           25         0.00025         75.2
   10          99,963           53         0.00053         67.4
   20          99,910          103         0.00103         64.5
   30          99,807          175         0.00175         49.3
   40          99,632          271         0.00272         37.3
   50          99,361          473         0.00476         25.4
   60          98,888          720         0.00728         17.5
   70          98,168          914         0.00931         10.0
   80          97,254        1,615         0.01661          0.0
   90          95,639        2,290         0.02394          3.1
  100          93,349        2,783         0.02981          3.5
  110          90,566       90,566         1.00000          4.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.85

The survival curve follows Gompertz law after age 30.
Data sourced from 205,825 death certificates.


Instruction: What are the mortality characteristics for infant population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 3.30 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 47%

Life table analysis shows high early risk.

Human: What are the mortality characteristics for infant population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 3.30 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 47%

Life table analysis shows high early risk.


Instruction: Summarize pension mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Pension Insurance
Study Period: 2020-2024
Exposure: 808759 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.89
• Deaths Actual: 5,041
• Deaths Expected: 7,622

BY DURATION:
• Select Period (Years 1-5): 0.74
• Ultimate (Years 6+): 1.10

Statistical confidence: 95% CI [0.84, 1.13]

Human: Summarize pension mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Pension Insurance
Study Period: 2020-2024
Exposure: 808759 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.89
• Deaths Actual: 5,041
• Deaths Expected: 7,622

BY DURATION:
• Select Period (Years 1-5): 0.74
• Ultimate (Years 6+): 1.10

Statistical confidence: 95% CI [0.84, 1.13]


Instruction: What is the mortality rate for Parkinson's in France for 45-64 in 2020?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Parkinson's
Location: France
Year: 2020
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 8.5 per 100,000 population
• Age-Adjusted Rate: 7.9 per 100,000
• Total Deaths: 225,050
• Percentage of All Deaths: 7.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 10.2 per 100,000
• Female Death Rate: 7.2 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: +13.4%
• 10-Year Change: +18.3%
• Annual Percentage Change: +0.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 2317676
• Economic Burden: $80.9 billion annually
• Preventable Deaths: 51%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): G20
Data Quality: Near-Complete (89% coverage)

Human: What is the mortality rate for Parkinson's in France for 45-64 in 2020?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Parkinson's
Location: France
Year: 2020
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 8.5 per 100,000 population
• Age-Adjusted Rate: 7.9 per 100,000
• Total Deaths: 225,050
• Percentage of All Deaths: 7.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 10.2 per 100,000
• Female Death Rate: 7.2 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: +13.4%
• 10-Year Change: +18.3%
• Annual Percentage Change: +0.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 2317676
• Economic Burden: $80.9 billion annually
• Preventable Deaths: 51%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): G20
Data Quality: Near-Complete (89% coverage)


Instruction: What is the life expectancy for a 55 year old both in Canada as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 55 years
• Sex: Both
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 55 (e_55): 24.0 years
• Expected Age at Death: 79.0 years
• Median Survival Time: 16.6 years
• Modal Age at Death: 74.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_55): 81.8%
• 10-Year Survival (₁₀p_55): 67.0%
• 20-Year Survival (₂₀p_55): 44.9%

MORTALITY METRICS:
• Force of Mortality (μ_55): 0.04006
• Probability of Death within 1 Year (q_55): 0.03927
• Hazard Rate: 0.04088

COMPARATIVE CONTEXT:
• Global Average at Age 55: 27.1 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 120,222 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.3%.

Human: What is the life expectancy for a 55 year old both in Canada as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 55 years
• Sex: Both
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 55 (e_55): 24.0 years
• Expected Age at Death: 79.0 years
• Median Survival Time: 16.6 years
• Modal Age at Death: 74.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_55): 81.8%
• 10-Year Survival (₁₀p_55): 67.0%
• 20-Year Survival (₂₀p_55): 44.9%

MORTALITY METRICS:
• Force of Mortality (μ_55): 0.04006
• Probability of Death within 1 Year (q_55): 0.03927
• Hazard Rate: 0.04088

COMPARATIVE CONTEXT:
• Global Average at Age 55: 27.1 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 120,222 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.3%.


Instruction: What is the probability of death within 1 year for someone age 61?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 61 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: diabetes, cancer history, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_61): 0.002419 (0.2419%)
• 1-Year Death Probability (₍1₎q_61): 0.002419 (0.242%)
• Survival Probability (₍1₎p_61): 0.997581 (99.758%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_61): 0.002421
• Hazard Rate (h_61): 0.002421
• Cumulative Hazard (H_61): 0.002421
• Median Future Lifetime: 286.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.4x standard
• Risk Category: Standard Plus
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 142%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.002056
• Upper Bound: 0.002781

Analysis based on 141,163 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 1 year for someone age 61?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 61 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: diabetes, cancer history, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_61): 0.002419 (0.2419%)
• 1-Year Death Probability (₍1₎q_61): 0.002419 (0.242%)
• Survival Probability (₍1₎p_61): 0.997581 (99.758%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_61): 0.002421
• Hazard Rate (h_61): 0.002421
• Cumulative Hazard (H_61): 0.002421
• Median Future Lifetime: 286.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.4x standard
• Risk Category: Standard Plus
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 142%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.002056
• Upper Bound: 0.002781

Analysis based on 141,163 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate mortality improvement factors for age 66

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 66
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.92%
• Current (2024): 1.71%
• Ultimate (2044+): 0.71%

PROJECTION FACTORS:
• 10-Year Factor: 0.8416
• 20-Year Factor: 0.7082
• 30-Year Factor: 0.5960

Cohort effect adjustment: Applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 66

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 66
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.92%
• Current (2024): 1.71%
• Ultimate (2044+): 0.71%

PROJECTION FACTORS:
• 10-Year Factor: 0.8416
• 20-Year Factor: 0.7082
• 30-Year Factor: 0.5960

Cohort effect adjustment: Applied
Gender-specific: No


Instruction: Analyze mortality patterns for 1924 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1924
Current Age: 100 years
Cohort Size at Birth: 2,697,381

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 73.0 years
• Current Life Expectancy: 87.3 years
• Survival to Current Age: 77.2%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 39.6 per 1,000
• Current Mortality Rate: 26.6 per 1,000
• Improvement Since Birth: 61%

Cohort effects explain 21% of mortality variation.

Human: Analyze mortality patterns for 1924 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1924
Current Age: 100 years
Cohort Size at Birth: 2,697,381

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 73.0 years
• Current Life Expectancy: 87.3 years
• Survival to Current Age: 77.2%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 39.6 per 1,000
• Current Mortality Rate: 26.6 per 1,000
• Improvement Since Birth: 61%

Cohort effects explain 21% of mortality variation.


Instruction: Show survival curve for China population in 2022

Response:
SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2022
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         83.3
    1          99,997           12         0.00012         81.1
    5          99,985           29         0.00029         77.3
   10          99,956           78         0.00078         67.7
   20          99,878          147         0.00147         58.4
   30          99,731          232         0.00233         49.4
   40          99,499          297         0.00298         43.8
   50          99,202          508         0.00512         35.0
   60          98,694          642         0.00650         15.8
   70          98,052          958         0.00977          8.1
   80          97,094        1,716         0.01767          2.0
   90          95,378        1,875         0.01966          1.5
  100          93,503        2,662         0.02847          4.0
  110          90,841       90,841         1.00000          3.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 97.1%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 362,372 death certificates.

Human: Show survival curve for China population in 2022

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2022
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         83.3
    1          99,997           12         0.00012         81.1
    5          99,985           29         0.00029         77.3
   10          99,956           78         0.00078         67.7
   20          99,878          147         0.00147         58.4
   30          99,731          232         0.00233         49.4
   40          99,499          297         0.00298         43.8
   50          99,202          508         0.00512         35.0
   60          98,694          642         0.00650         15.8
   70          98,052          958         0.00977          8.1
   80          97,094        1,716         0.01767          2.0
   90          95,378        1,875         0.01966          1.5
  100          93,503        2,662         0.02847          4.0
  110          90,841       90,841         1.00000          3.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 97.1%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 362,372 death certificates.


Instruction: Calculate Whole Life life insurance premium for 41 year old female, $1,000,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 41
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_41): 0.001541
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 72% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3235.09
• Expense Charge: $808.77
• Reserve Accumulation: $1078.36
• Profit Margin: $269.59
• Gross Annual Premium: $5391.82

PAYMENT OPTIONS:
• Annual: $5391.82
• Semi-Annual: $2803.75 (x2 = $5607.50/year)
• Quarterly: $1428.83 (x4 = $5715.33/year)
• Monthly: $485.26 (x12 = $5823.17/year)

RESERVE CALCULATIONS:
• Net Level Premium: $4043.87
• First Year Reserve: $1078.36
• Terminal Reserve (Year 24): $391366.42

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 9.1%
Profit Margin: 12.2%
Lapse Assumption: 4.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 41 year old female, $1,000,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 41
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_41): 0.001541
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 72% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3235.09
• Expense Charge: $808.77
• Reserve Accumulation: $1078.36
• Profit Margin: $269.59
• Gross Annual Premium: $5391.82

PAYMENT OPTIONS:
• Annual: $5391.82
• Semi-Annual: $2803.75 (x2 = $5607.50/year)
• Quarterly: $1428.83 (x4 = $5715.33/year)
• Monthly: $485.26 (x12 = $5823.17/year)

RESERVE CALCULATIONS:
• Net Level Premium: $4043.87
• First Year Reserve: $1078.36
• Terminal Reserve (Year 24): $391366.42

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 9.1%
Profit Margin: 12.2%
Lapse Assumption: 4.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate excess mortality during seasonal flu in USA for Q4 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: USA
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 70,722
• Observed Deaths: 103,213
• Excess Deaths: 32,491
• Excess Mortality Rate: 45.9%
• P-score: 45.9%
• Z-score: 2.02 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.2% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 6.2% (3,249 deaths)
• 45-64 years: 5.4% (8,122 deaths)
• 65-74 years: 25.7% (8,122 deaths)
• 75+ years: 22.0% (12,996 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 24,922 (74%)
• Indirect (probable): 8,759 (24%)
• Collateral (delayed care): 4,085 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [27,617, 37,364]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 366822
Economic Impact: $3.7 billion
Quality-Adjusted Life Years Lost: 262102

Human: Calculate excess mortality during seasonal flu in USA for Q4 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: USA
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 70,722
• Observed Deaths: 103,213
• Excess Deaths: 32,491
• Excess Mortality Rate: 45.9%
• P-score: 45.9%
• Z-score: 2.02 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.2% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 6.2% (3,249 deaths)
• 45-64 years: 5.4% (8,122 deaths)
• 65-74 years: 25.7% (8,122 deaths)
• 75+ years: 22.0% (12,996 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 24,922 (74%)
• Indirect (probable): 8,759 (24%)
• Collateral (delayed care): 4,085 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [27,617, 37,364]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 366822
Economic Impact: $3.7 billion
Quality-Adjusted Life Years Lost: 262102


Instruction: Project mortality rates for Germany in 2030

Response:
MORTALITY PROJECTION

Country: Germany
Target Year: 2030
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 805.0 per 100,000
• Life Expectancy: 89.3 years
• Annual Improvement: 1.93%

CONFIDENCE INTERVALS (95%):
• Lower: 684.2
• Upper: 925.7

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.

Human: Project mortality rates for Germany in 2030

Actuarial AI: MORTALITY PROJECTION

Country: Germany
Target Year: 2030
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 805.0 per 100,000
• Life Expectancy: 89.3 years
• Annual Improvement: 1.93%

CONFIDENCE INTERVALS (95%):
• Lower: 684.2
• Upper: 925.7

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.


Instruction: Show survival curve for Brazil male in 2018

Response:
SURVIVAL CURVE ANALYSIS

Population: Brazil Male
Reference Year: 2018
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.2
    1          99,997           14         0.00014         78.1
    5          99,983           25         0.00025         70.3
   10          99,958           88         0.00088         71.0
   20          99,870          166         0.00166         58.2
   30          99,704          256         0.00257         54.3
   40          99,448          449         0.00451         42.8
   50          98,999          756         0.00764         25.8
   60          98,243          954         0.00971         18.7
   70          97,289        1,618         0.01663         15.0
   80          95,671        1,655         0.01730          3.1
   90          94,016        3,040         0.03233          3.3
  100          90,976        3,090         0.03397          3.8
  110          87,886       87,886         1.00000          2.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.2%
• Probability of Surviving to 80: 95.7%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.86

The survival curve follows Gompertz law after age 30.
Data sourced from 120,775 death certificates.

Human: Show survival curve for Brazil male in 2018

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Brazil Male
Reference Year: 2018
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.2
    1          99,997           14         0.00014         78.1
    5          99,983           25         0.00025         70.3
   10          99,958           88         0.00088         71.0
   20          99,870          166         0.00166         58.2
   30          99,704          256         0.00257         54.3
   40          99,448          449         0.00451         42.8
   50          98,999          756         0.00764         25.8
   60          98,243          954         0.00971         18.7
   70          97,289        1,618         0.01663         15.0
   80          95,671        1,655         0.01730          3.1
   90          94,016        3,040         0.03233          3.3
  100          90,976        3,090         0.03397          3.8
  110          87,886       87,886         1.00000          2.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.2%
• Probability of Surviving to 80: 95.7%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.86

The survival curve follows Gompertz law after age 30.
Data sourced from 120,775 death certificates.


Instruction: Calculate policy reserve for 48 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 38
• Current Age: 48
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1156.74
• Present Value Future Benefits (PVFB): $56839.93
• Present Value Future Premiums (PVFP): $35271.39

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $27957.09
• Per $1,000 Face: $279.57

PROSPECTIVE METHOD:
• A₁_48:10⌉ = 0.2287
• ä_48:10⌉ = 9.5698
• ₁₀V = 100,000 × A₁ - P × ä = $27957.09

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9330.65
• Accumulated Cost of Insurance: $5118.11
• Interest Earned: $1899.17
• ₁₀V = $27957.09

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $26559.23
• Tax Reserve: $25720.52
• GAAP Reserve: $29354.94

Human: Calculate policy reserve for 48 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 38
• Current Age: 48
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1156.74
• Present Value Future Benefits (PVFB): $56839.93
• Present Value Future Premiums (PVFP): $35271.39

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $27957.09
• Per $1,000 Face: $279.57

PROSPECTIVE METHOD:
• A₁_48:10⌉ = 0.2287
• ä_48:10⌉ = 9.5698
• ₁₀V = 100,000 × A₁ - P × ä = $27957.09

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9330.65
• Accumulated Cost of Insurance: $5118.11
• Interest Earned: $1899.17
• ₁₀V = $27957.09

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $26559.23
• Tax Reserve: $25720.52
• GAAP Reserve: $29354.94


Instruction: Mortality risk assessment for 72 year old over next 5 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 72 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension, obesity, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_72): 0.009396 (0.9396%)
• 5-Year Death Probability (₍5₎q_72): 0.046105 (4.611%)
• Survival Probability (₍5₎p_72): 0.953895 (95.389%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_72): 0.009440
• Hazard Rate (h_72): 0.009440
• Cumulative Hazard (H_72): 0.047202
• Median Future Lifetime: 73.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 9.4x standard
• Risk Category: Substandard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 840%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.039189
• Upper Bound: 0.053021

Analysis based on 199,196 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 72 year old over next 5 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 72 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension, obesity, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_72): 0.009396 (0.9396%)
• 5-Year Death Probability (₍5₎q_72): 0.046105 (4.611%)
• Survival Probability (₍5₎p_72): 0.953895 (95.389%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_72): 0.009440
• Hazard Rate (h_72): 0.009440
• Cumulative Hazard (H_72): 0.047202
• Median Future Lifetime: 73.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 9.4x standard
• Risk Category: Substandard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 840%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.039189
• Upper Bound: 0.053021

Analysis based on 199,196 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate excess mortality during opioid crisis in USA for 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: USA
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 17,738
• Observed Deaths: 26,230
• Excess Deaths: 8,492
• Excess Mortality Rate: 47.9%
• P-score: 47.9%
• Z-score: 4.06 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 7.5% (849 deaths)
• 45-64 years: 9.3% (2,123 deaths)
• 65-74 years: 13.5% (2,123 deaths)
• 75+ years: 30.7% (3,396 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 6,175 (57%)
• Indirect (probable): 2,323 (19%)
• Collateral (delayed care): 1,545 (18%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [7,218, 9,765]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 89295
Economic Impact: $4.8 billion
Quality-Adjusted Life Years Lost: 68724

Human: Calculate excess mortality during opioid crisis in USA for 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: USA
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 17,738
• Observed Deaths: 26,230
• Excess Deaths: 8,492
• Excess Mortality Rate: 47.9%
• P-score: 47.9%
• Z-score: 4.06 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 7.5% (849 deaths)
• 45-64 years: 9.3% (2,123 deaths)
• 65-74 years: 13.5% (2,123 deaths)
• 75+ years: 30.7% (3,396 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 6,175 (57%)
• Indirect (probable): 2,323 (19%)
• Collateral (delayed care): 1,545 (18%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [7,218, 9,765]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 89295
Economic Impact: $4.8 billion
Quality-Adjusted Life Years Lost: 68724


Instruction: Analyze mortality patterns for 1956 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1956
Current Age: 68 years
Cohort Size at Birth: 3,726,329

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 73.0 years
• Current Life Expectancy: 89.3 years
• Survival to Current Age: 75.3%

HISTORICAL EXPOSURES:
• High smoking prevalence
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 42.1 per 1,000
• Current Mortality Rate: 11.0 per 1,000
• Improvement Since Birth: 37%

Cohort effects explain 25% of mortality variation.

Human: Analyze mortality patterns for 1956 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1956
Current Age: 68 years
Cohort Size at Birth: 3,726,329

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 73.0 years
• Current Life Expectancy: 89.3 years
• Survival to Current Age: 75.3%

HISTORICAL EXPOSURES:
• High smoking prevalence
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 42.1 per 1,000
• Current Mortality Rate: 11.0 per 1,000
• Improvement Since Birth: 37%

Cohort effects explain 25% of mortality variation.


Instruction: Compare cardiovascular mortality between Russia, Brazil, Spain, USA and Canada

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Russia, Brazil, Spain, USA, Canada
Reference Year: 2020

COMPARATIVE STATISTICS:
• Russia: 138.2 per 100,000 population
• Brazil: 188.9 per 100,000 population
• Spain: 208.4 per 100,000 population
• USA: 78.2 per 100,000 population
• Canada: 198.8 per 100,000 population

RANKINGS:
1. USA: 78.2
2. Russia: 138.2
3. Brazil: 188.9
4. Canada: 198.8
5. Spain: 208.4

STATISTICAL ANALYSIS:
• Range: 130.2
• Mean: 162.5
• Median: 188.9
• Standard Deviation: 48.6
• Coefficient of Variation: 29.9%

RELATIVE COMPARISONS:
• Best vs Worst: 2.66x difference
• Above Average: 3/5
• Global Ranking: Russia: #184, Brazil: #157, Spain: #127

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 20% of variation
• Public Health Policy: 14% of variation
• Demographics: 18% of variation
• Environmental Factors: 5% of variation

Convergence/Divergence: Converging at 0.9% annually

Human: Compare cardiovascular mortality between Russia, Brazil, Spain, USA and Canada

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Russia, Brazil, Spain, USA, Canada
Reference Year: 2020

COMPARATIVE STATISTICS:
• Russia: 138.2 per 100,000 population
• Brazil: 188.9 per 100,000 population
• Spain: 208.4 per 100,000 population
• USA: 78.2 per 100,000 population
• Canada: 198.8 per 100,000 population

RANKINGS:
1. USA: 78.2
2. Russia: 138.2
3. Brazil: 188.9
4. Canada: 198.8
5. Spain: 208.4

STATISTICAL ANALYSIS:
• Range: 130.2
• Mean: 162.5
• Median: 188.9
• Standard Deviation: 48.6
• Coefficient of Variation: 29.9%

RELATIVE COMPARISONS:
• Best vs Worst: 2.66x difference
• Above Average: 3/5
• Global Ranking: Russia: #184, Brazil: #157, Spain: #127

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 20% of variation
• Public Health Policy: 14% of variation
• Demographics: 18% of variation
• Environmental Factors: 5% of variation

Convergence/Divergence: Converging at 0.9% annually


Instruction: Calculate Universal Life life insurance premium for 59 year old male, $250,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 59
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_59): 0.004220
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 52% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1772.27
• Expense Charge: $443.07
• Reserve Accumulation: $590.76
• Profit Margin: $147.69
• Gross Annual Premium: $2953.78

PAYMENT OPTIONS:
• Annual: $2953.78
• Semi-Annual: $1535.97 (x2 = $3071.94/year)
• Quarterly: $782.75 (x4 = $3131.01/year)
• Monthly: $265.84 (x12 = $3190.09/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2215.34
• First Year Reserve: $590.76
• Terminal Reserve (Year 6): $79817.69

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 8.5%
Profit Margin: 14.6%
Lapse Assumption: 7.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 59 year old male, $250,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 59
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_59): 0.004220
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 52% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1772.27
• Expense Charge: $443.07
• Reserve Accumulation: $590.76
• Profit Margin: $147.69
• Gross Annual Premium: $2953.78

PAYMENT OPTIONS:
• Annual: $2953.78
• Semi-Annual: $1535.97 (x2 = $3071.94/year)
• Quarterly: $782.75 (x4 = $3131.01/year)
• Monthly: $265.84 (x12 = $3190.09/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2215.34
• First Year Reserve: $590.76
• Terminal Reserve (Year 6): $79817.69

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 8.5%
Profit Margin: 14.6%
Lapse Assumption: 7.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate policy reserve for 54 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 44
• Current Age: 54
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $550.16
• Present Value Future Benefits (PVFB): $43124.45
• Present Value Future Premiums (PVFP): $35908.08

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $38685.96
• Per $1,000 Face: $386.86

PROSPECTIVE METHOD:
• A₁_54:10⌉ = 0.1605
• ä_54:10⌉ = 8.5336
• ₁₀V = 100,000 × A₁ - P × ä = $38685.96

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8967.13
• Accumulated Cost of Insurance: $4760.53
• Interest Earned: $1607.17
• ₁₀V = $38685.96

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $36751.67
• Tax Reserve: $35591.09
• GAAP Reserve: $40620.26

Human: Calculate policy reserve for 54 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 44
• Current Age: 54
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $550.16
• Present Value Future Benefits (PVFB): $43124.45
• Present Value Future Premiums (PVFP): $35908.08

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $38685.96
• Per $1,000 Face: $386.86

PROSPECTIVE METHOD:
• A₁_54:10⌉ = 0.1605
• ä_54:10⌉ = 8.5336
• ₁₀V = 100,000 × A₁ - P × ä = $38685.96

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8967.13
• Accumulated Cost of Insurance: $4760.53
• Interest Earned: $1607.17
• ₁₀V = $38685.96

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $36751.67
• Tax Reserve: $35591.09
• GAAP Reserve: $40620.26


Instruction: Mortality risk assessment for 63 year old over next 20 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 63 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_63): 0.000985 (0.0985%)
• 20-Year Death Probability (₍20₎q_63): 0.019516 (1.952%)
• Survival Probability (₍20₎p_63): 0.980484 (98.048%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_63): 0.000985
• Hazard Rate (h_63): 0.000985
• Cumulative Hazard (H_63): 0.019709
• Median Future Lifetime: 703.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.0x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016588
• Upper Bound: 0.022443

Analysis based on 174,045 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 63 year old over next 20 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 63 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_63): 0.000985 (0.0985%)
• 20-Year Death Probability (₍20₎q_63): 0.019516 (1.952%)
• Survival Probability (₍20₎p_63): 0.980484 (98.048%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_63): 0.000985
• Hazard Rate (h_63): 0.000985
• Cumulative Hazard (H_63): 0.019709
• Median Future Lifetime: 703.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.0x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016588
• Upper Bound: 0.022443

Analysis based on 174,045 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Compare infant mortality between Canada, Germany, UK and Brazil

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Canada, Germany, UK, Brazil
Reference Year: 2021

COMPARATIVE STATISTICS:
• Canada: 12.9 per 1,000 live births
• Germany: 7.8 per 1,000 live births
• UK: 24.4 per 1,000 live births
• Brazil: 14.6 per 1,000 live births

RANKINGS:
1. Germany: 7.8
2. Canada: 12.9
3. Brazil: 14.6
4. UK: 24.4

STATISTICAL ANALYSIS:
• Range: 16.6
• Mean: 14.9
• Median: 13.8
• Standard Deviation: 6.0
• Coefficient of Variation: 40.3%

RELATIVE COMPARISONS:
• Best vs Worst: 3.14x difference
• Above Average: 1/4
• Global Ranking: Canada: #154, Germany: #27, UK: #8

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 35% of variation
• Public Health Policy: 24% of variation
• Demographics: 14% of variation
• Environmental Factors: 8% of variation

Convergence/Divergence: Diverging at 1.2% annually

Human: Compare infant mortality between Canada, Germany, UK and Brazil

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Canada, Germany, UK, Brazil
Reference Year: 2021

COMPARATIVE STATISTICS:
• Canada: 12.9 per 1,000 live births
• Germany: 7.8 per 1,000 live births
• UK: 24.4 per 1,000 live births
• Brazil: 14.6 per 1,000 live births

RANKINGS:
1. Germany: 7.8
2. Canada: 12.9
3. Brazil: 14.6
4. UK: 24.4

STATISTICAL ANALYSIS:
• Range: 16.6
• Mean: 14.9
• Median: 13.8
• Standard Deviation: 6.0
• Coefficient of Variation: 40.3%

RELATIVE COMPARISONS:
• Best vs Worst: 3.14x difference
• Above Average: 1/4
• Global Ranking: Canada: #154, Germany: #27, UK: #8

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 35% of variation
• Public Health Policy: 24% of variation
• Demographics: 14% of variation
• Environmental Factors: 8% of variation

Convergence/Divergence: Diverging at 1.2% annually


Instruction: Show survival curve for Canada female in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         76.9
    1          99,998           11         0.00011         83.3
    5          99,987           23         0.00023         74.3
   10          99,964           66         0.00066         70.7
   20          99,898          117         0.00117         64.0
   30          99,781          182         0.00182         46.3
   40          99,599          317         0.00318         35.8
   50          99,282          457         0.00460         31.1
   60          98,825          705         0.00713         23.5
   70          98,120          879         0.00896         13.1
   80          97,241        1,560         0.01604          0.8
   90          95,681        1,877         0.01962          5.0
  100          93,804        2,847         0.03035          1.6
  110          90,957       90,957         1.00000          2.4

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.2%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 124,438 death certificates.

Human: Show survival curve for Canada female in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         76.9
    1          99,998           11         0.00011         83.3
    5          99,987           23         0.00023         74.3
   10          99,964           66         0.00066         70.7
   20          99,898          117         0.00117         64.0
   30          99,781          182         0.00182         46.3
   40          99,599          317         0.00318         35.8
   50          99,282          457         0.00460         31.1
   60          98,825          705         0.00713         23.5
   70          98,120          879         0.00896         13.1
   80          97,241        1,560         0.01604          0.8
   90          95,681        1,877         0.01962          5.0
  100          93,804        2,847         0.03035          1.6
  110          90,957       90,957         1.00000          2.4

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.2%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 124,438 death certificates.


Instruction: Compare cancer mortality between Germany and Italy

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Germany, Italy
Reference Year: 2023

COMPARATIVE STATISTICS:
• Germany: 57.4 per 100,000 population
• Italy: 127.7 per 100,000 population

RANKINGS:
1. Germany: 57.4
2. Italy: 127.7

STATISTICAL ANALYSIS:
• Range: 70.3
• Mean: 92.6
• Median: 92.6
• Standard Deviation: 35.2
• Coefficient of Variation: 38.0%

RELATIVE COMPARISONS:
• Best vs Worst: 2.22x difference
• Above Average: 1/2
• Global Ranking: Germany: #179, Italy: #6

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 27% of variation
• Public Health Policy: 22% of variation
• Demographics: 11% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Diverging at 1.3% annually

Human: Compare cancer mortality between Germany and Italy

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Germany, Italy
Reference Year: 2023

COMPARATIVE STATISTICS:
• Germany: 57.4 per 100,000 population
• Italy: 127.7 per 100,000 population

RANKINGS:
1. Germany: 57.4
2. Italy: 127.7

STATISTICAL ANALYSIS:
• Range: 70.3
• Mean: 92.6
• Median: 92.6
• Standard Deviation: 35.2
• Coefficient of Variation: 38.0%

RELATIVE COMPARISONS:
• Best vs Worst: 2.22x difference
• Above Average: 1/2
• Global Ranking: Germany: #179, Italy: #6

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 27% of variation
• Public Health Policy: 22% of variation
• Demographics: 11% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Diverging at 1.3% annually


Instruction: Show survival curve for USA female in 2015

Response:
SURVIVAL CURVE ANALYSIS

Population: USA Female
Reference Year: 2015
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         75.1
    1          99,998            8         0.00008         75.5
    5          99,990           27         0.00027         79.5
   10          99,963           55         0.00055         67.5
   20          99,908          110         0.00110         59.6
   30          99,798          158         0.00158         45.9
   40          99,640          278         0.00279         45.0
   50          99,362          527         0.00530         31.1
   60          98,835          615         0.00622         23.1
   70          98,220          966         0.00984         12.0
   80          97,254        1,170         0.01203          0.8
   90          96,084        2,384         0.02481          4.8
  100          93,700        2,389         0.02550          1.6
  110          91,311       91,311         1.00000          3.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.89

The survival curve follows Gompertz law after age 30.
Data sourced from 459,146 death certificates.

Human: Show survival curve for USA female in 2015

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: USA Female
Reference Year: 2015
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         75.1
    1          99,998            8         0.00008         75.5
    5          99,990           27         0.00027         79.5
   10          99,963           55         0.00055         67.5
   20          99,908          110         0.00110         59.6
   30          99,798          158         0.00158         45.9
   40          99,640          278         0.00279         45.0
   50          99,362          527         0.00530         31.1
   60          98,835          615         0.00622         23.1
   70          98,220          966         0.00984         12.0
   80          97,254        1,170         0.01203          0.8
   90          96,084        2,384         0.02481          4.8
  100          93,700        2,389         0.02550          1.6
  110          91,311       91,311         1.00000          3.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.89

The survival curve follows Gompertz law after age 30.
Data sourced from 459,146 death certificates.


Instruction: Calculate Term life insurance premium for 60 year old female, $250,000 coverage, 15 year term, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 60
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.002418
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 91% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $362.77
• Expense Charge: $90.69
• Reserve Accumulation: $120.92
• Profit Margin: $30.23
• Gross Annual Premium: $604.62

PAYMENT OPTIONS:
• Annual: $604.62
• Semi-Annual: $314.40 (x2 = $628.80/year)
• Quarterly: $160.22 (x4 = $640.89/year)
• Monthly: $54.42 (x12 = $652.99/year)

RESERVE CALCULATIONS:
• Net Level Premium: $453.46
• First Year Reserve: $120.92
• Terminal Reserve (Year 15): $141221.85

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.1%
Profit Margin: 9.6%
Lapse Assumption: 3.8% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 60 year old female, $250,000 coverage, 15 year term, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 60
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.002418
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 91% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $362.77
• Expense Charge: $90.69
• Reserve Accumulation: $120.92
• Profit Margin: $30.23
• Gross Annual Premium: $604.62

PAYMENT OPTIONS:
• Annual: $604.62
• Semi-Annual: $314.40 (x2 = $628.80/year)
• Quarterly: $160.22 (x4 = $640.89/year)
• Monthly: $54.42 (x12 = $652.99/year)

RESERVE CALCULATIONS:
• Net Level Premium: $453.46
• First Year Reserve: $120.92
• Terminal Reserve (Year 15): $141221.85

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.1%
Profit Margin: 9.6%
Lapse Assumption: 3.8% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare rural vs other area mortality rates in USA

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 804.2
• Rural: 907.6
• Suburban: 741.8

Rural areas show 12.9% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare rural vs other area mortality rates in USA

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 804.2
• Rural: 907.6
• Suburban: 741.8

Rural areas show 12.9% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: What is the life expectancy for a 66 year old both in China as of 2024?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 66 years
• Sex: Both
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 66 (e_66): 11.7 years
• Expected Age at Death: 77.7 years
• Median Survival Time: 8.1 years
• Modal Age at Death: 72.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_66): 67.4%
• 10-Year Survival (₁₀p_66): 45.5%
• 20-Year Survival (₂₀p_66): 20.7%

MORTALITY METRICS:
• Force of Mortality (μ_66): 0.07880
• Probability of Death within 1 Year (q_66): 0.07577
• Hazard Rate: 0.08208

COMPARATIVE CONTEXT:
• Global Average at Age 66: 10.9 years
• Regional Rank: Top 35 globally
• Historical Trend: Stable

Based on 442,047 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.

Human: What is the life expectancy for a 66 year old both in China as of 2024?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 66 years
• Sex: Both
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 66 (e_66): 11.7 years
• Expected Age at Death: 77.7 years
• Median Survival Time: 8.1 years
• Modal Age at Death: 72.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_66): 67.4%
• 10-Year Survival (₁₀p_66): 45.5%
• 20-Year Survival (₂₀p_66): 20.7%

MORTALITY METRICS:
• Force of Mortality (μ_66): 0.07880
• Probability of Death within 1 Year (q_66): 0.07577
• Hazard Rate: 0.08208

COMPARATIVE CONTEXT:
• Global Average at Age 66: 10.9 years
• Regional Rank: Top 35 globally
• Historical Trend: Stable

Based on 442,047 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.


Instruction: Compare infant mortality between Brazil, South Korea, Mexico and Australia

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Brazil, South Korea, Mexico, Australia
Reference Year: 2020

COMPARATIVE STATISTICS:
• Brazil: 14.8 per 1,000 live births
• South Korea: 27.7 per 1,000 live births
• Mexico: 3.6 per 1,000 live births
• Australia: 17.0 per 1,000 live births

RANKINGS:
1. Mexico: 3.6
2. Brazil: 14.8
3. Australia: 17.0
4. South Korea: 27.7

STATISTICAL ANALYSIS:
• Range: 24.1
• Mean: 15.8
• Median: 15.9
• Standard Deviation: 8.6
• Coefficient of Variation: 54.4%

RELATIVE COMPARISONS:
• Best vs Worst: 7.80x difference
• Above Average: 2/4
• Global Ranking: Brazil: #89, South Korea: #48, Mexico: #30

CONTRIBUTING FACTORS:
• Healthcare System: 39% of variation
• Economic Development: 35% of variation
• Public Health Policy: 17% of variation
• Demographics: 19% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Converging at 1.8% annually

Human: Compare infant mortality between Brazil, South Korea, Mexico and Australia

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Brazil, South Korea, Mexico, Australia
Reference Year: 2020

COMPARATIVE STATISTICS:
• Brazil: 14.8 per 1,000 live births
• South Korea: 27.7 per 1,000 live births
• Mexico: 3.6 per 1,000 live births
• Australia: 17.0 per 1,000 live births

RANKINGS:
1. Mexico: 3.6
2. Brazil: 14.8
3. Australia: 17.0
4. South Korea: 27.7

STATISTICAL ANALYSIS:
• Range: 24.1
• Mean: 15.8
• Median: 15.9
• Standard Deviation: 8.6
• Coefficient of Variation: 54.4%

RELATIVE COMPARISONS:
• Best vs Worst: 7.80x difference
• Above Average: 2/4
• Global Ranking: Brazil: #89, South Korea: #48, Mexico: #30

CONTRIBUTING FACTORS:
• Healthcare System: 39% of variation
• Economic Development: 35% of variation
• Public Health Policy: 17% of variation
• Demographics: 19% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Converging at 1.8% annually


Instruction: Show survival curve for Canada female in 2015

Response:
SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2015
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         79.5
    1          99,998           12         0.00012         82.8
    5          99,986           23         0.00023         72.6
   10          99,963           50         0.00050         67.3
   20          99,913           87         0.00087         56.2
   30          99,826          218         0.00218         49.2
   40          99,608          311         0.00312         41.8
   50          99,297          415         0.00418         30.3
   60          98,882          754         0.00763         15.8
   70          98,128          993         0.01012         10.6
   80          97,135        1,592         0.01639          2.1
   90          95,543        2,148         0.02248          4.8
  100          93,395        2,463         0.02637          1.9
  110          90,932       90,932         1.00000          3.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.1%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 435,721 death certificates.

Human: Show survival curve for Canada female in 2015

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2015
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         79.5
    1          99,998           12         0.00012         82.8
    5          99,986           23         0.00023         72.6
   10          99,963           50         0.00050         67.3
   20          99,913           87         0.00087         56.2
   30          99,826          218         0.00218         49.2
   40          99,608          311         0.00312         41.8
   50          99,297          415         0.00418         30.3
   60          98,882          754         0.00763         15.8
   70          98,128          993         0.01012         10.6
   80          97,135        1,592         0.01639          2.1
   90          95,543        2,148         0.02248          4.8
  100          93,395        2,463         0.02637          1.9
  110          90,932       90,932         1.00000          3.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.1%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 435,721 death certificates.


Instruction: What is the mortality rate for Accidents in UK for 75+ in 2021?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Accidents
Location: UK
Year: 2021
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 64.0 per 100,000 population
• Age-Adjusted Rate: 55.3 per 100,000
• Total Deaths: 1,546,578
• Percentage of All Deaths: 10.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 76.8 per 100,000
• Female Death Rate: 54.4 per 100,000
• Sex Ratio (M:F): 1.24:1

TREND ANALYSIS:
• 5-Year Change: +2.8%
• 10-Year Change: +12.8%
• Annual Percentage Change: -1.3%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 42525297
• Economic Burden: $90.9 billion annually
• Preventable Deaths: 20%

RISK FACTORS:
• Motor vehicle: 35% of total
• Falls: 30%
• Poisoning: 25%
• Drowning: 5%
• Fire: 3%

International Classification of Diseases (ICD-10): V01-X59
Data Quality: Complete (97% coverage)

Human: What is the mortality rate for Accidents in UK for 75+ in 2021?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Accidents
Location: UK
Year: 2021
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 64.0 per 100,000 population
• Age-Adjusted Rate: 55.3 per 100,000
• Total Deaths: 1,546,578
• Percentage of All Deaths: 10.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 76.8 per 100,000
• Female Death Rate: 54.4 per 100,000
• Sex Ratio (M:F): 1.24:1

TREND ANALYSIS:
• 5-Year Change: +2.8%
• 10-Year Change: +12.8%
• Annual Percentage Change: -1.3%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 42525297
• Economic Burden: $90.9 billion annually
• Preventable Deaths: 20%

RISK FACTORS:
• Motor vehicle: 35% of total
• Falls: 30%
• Poisoning: 25%
• Drowning: 5%
• Fire: 3%

International Classification of Diseases (ICD-10): V01-X59
Data Quality: Complete (97% coverage)