Instruction: Project mortality rates for Germany in 2050

Response:
MORTALITY PROJECTION

Country: Germany
Target Year: 2050
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 578.9 per 100,000
• Life Expectancy: 88.4 years
• Annual Improvement: 1.80%

CONFIDENCE INTERVALS (95%):
• Lower: 492.1
• Upper: 665.7

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

Human: Project mortality rates for Germany in 2050

Actuarial AI: MORTALITY PROJECTION

Country: Germany
Target Year: 2050
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 578.9 per 100,000
• Life Expectancy: 88.4 years
• Annual Improvement: 1.80%

CONFIDENCE INTERVALS (95%):
• Lower: 492.1
• Upper: 665.7

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


Instruction: Calculate Variable Universal Life life insurance premium for 23 year old female, $250,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 23
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_23): 0.000564
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 85% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $211.36
• Expense Charge: $52.84
• Reserve Accumulation: $70.45
• Profit Margin: $17.61
• Gross Annual Premium: $352.27

PAYMENT OPTIONS:
• Annual: $352.27
• Semi-Annual: $183.18 (x2 = $366.36/year)
• Quarterly: $93.35 (x4 = $373.41/year)
• Monthly: $31.70 (x12 = $380.46/year)

RESERVE CALCULATIONS:
• Net Level Premium: $264.20
• First Year Reserve: $70.45
• Terminal Reserve (Year 42): $116778.28

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

Internal Rate of Return: 11.5%
Profit Margin: 13.3%
Lapse Assumption: 7.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 23 year old female, $250,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 23
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_23): 0.000564
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 85% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $211.36
• Expense Charge: $52.84
• Reserve Accumulation: $70.45
• Profit Margin: $17.61
• Gross Annual Premium: $352.27

PAYMENT OPTIONS:
• Annual: $352.27
• Semi-Annual: $183.18 (x2 = $366.36/year)
• Quarterly: $93.35 (x4 = $373.41/year)
• Monthly: $31.70 (x12 = $380.46/year)

RESERVE CALCULATIONS:
• Net Level Premium: $264.20
• First Year Reserve: $70.45
• Terminal Reserve (Year 42): $116778.28

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

Internal Rate of Return: 11.5%
Profit Margin: 13.3%
Lapse Assumption: 7.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate policy reserve for 42 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: 32
• Current Age: 42
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $902.27
• Present Value Future Benefits (PVFB): $41559.57
• Present Value Future Premiums (PVFP): $26864.92

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $28721.34
• Per $1,000 Face: $287.21

PROSPECTIVE METHOD:
• A₁_42:10⌉ = 0.1766
• ä_42:10⌉ = 9.0634
• ₁₀V = 100,000 × A₁ - P × ä = $28721.34

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11190.66
• Accumulated Cost of Insurance: $3266.01
• Interest Earned: $1301.31
• ₁₀V = $28721.34

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $27285.27
• Tax Reserve: $26423.63
• GAAP Reserve: $30157.40

Human: Calculate policy reserve for 42 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: 32
• Current Age: 42
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $902.27
• Present Value Future Benefits (PVFB): $41559.57
• Present Value Future Premiums (PVFP): $26864.92

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $28721.34
• Per $1,000 Face: $287.21

PROSPECTIVE METHOD:
• A₁_42:10⌉ = 0.1766
• ä_42:10⌉ = 9.0634
• ₁₀V = 100,000 × A₁ - P × ä = $28721.34

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11190.66
• Accumulated Cost of Insurance: $3266.01
• Interest Earned: $1301.31
• ₁₀V = $28721.34

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $27285.27
• Tax Reserve: $26423.63
• GAAP Reserve: $30157.40


Instruction: Analyze mortality differences by education in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Education
Country: USA
Analysis Period: 2019

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 885.2
• High School: 379.2
• Some College: 778.1
• Bachelor's: 205.1
• Graduate Degree: 1107.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.77
• Rate Difference: 765.1 per 100,000
• Population Attributable Risk: 33.9%
• Gini Coefficient: 0.257

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 84.9 years
• High School: 78.4 years
• Some College: 77.4 years
• Bachelor's: 78.3 years
• Graduate Degree: 78.8 years

CONTRIBUTING FACTORS:
• Healthcare Access: 30% of disparity
• Socioeconomic Status: 34% of disparity
• Environmental Factors: 20% of disparity
• Behavioral Factors: 18% of disparity
• Biological Factors: 13% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -1.7%

Social determinants explain 61% of observed mortality differences.

Human: Analyze mortality differences by education in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Education
Country: USA
Analysis Period: 2019

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 885.2
• High School: 379.2
• Some College: 778.1
• Bachelor's: 205.1
• Graduate Degree: 1107.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.77
• Rate Difference: 765.1 per 100,000
• Population Attributable Risk: 33.9%
• Gini Coefficient: 0.257

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 84.9 years
• High School: 78.4 years
• Some College: 77.4 years
• Bachelor's: 78.3 years
• Graduate Degree: 78.8 years

CONTRIBUTING FACTORS:
• Healthcare Access: 30% of disparity
• Socioeconomic Status: 34% of disparity
• Environmental Factors: 20% of disparity
• Behavioral Factors: 18% of disparity
• Biological Factors: 13% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -1.7%

Social determinants explain 61% of observed mortality differences.


Instruction: Show survival curve for Japan female in 2022

Response:
SURVIVAL CURVE ANALYSIS

Population: Japan Female
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            2         0.00002         81.5
    1          99,998            9         0.00009         81.3
    5          99,989           26         0.00026         72.9
   10          99,963           63         0.00063         65.3
   20          99,900          108         0.00108         62.2
   30          99,792          167         0.00167         51.0
   40          99,625          353         0.00354         37.7
   50          99,272          533         0.00537         34.9
   60          98,739          784         0.00794         21.4
   70          97,955          998         0.01019          6.6
   80          96,957        1,158         0.01194          0.0
   90          95,799        2,055         0.02145          4.4
  100          93,744        3,205         0.03419          2.7
  110          90,539       90,539         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.85

The survival curve follows Gompertz law after age 30.
Data sourced from 235,082 death certificates.

Human: Show survival curve for Japan female in 2022

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Japan Female
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            2         0.00002         81.5
    1          99,998            9         0.00009         81.3
    5          99,989           26         0.00026         72.9
   10          99,963           63         0.00063         65.3
   20          99,900          108         0.00108         62.2
   30          99,792          167         0.00167         51.0
   40          99,625          353         0.00354         37.7
   50          99,272          533         0.00537         34.9
   60          98,739          784         0.00794         21.4
   70          97,955          998         0.01019          6.6
   80          96,957        1,158         0.01194          0.0
   90          95,799        2,055         0.02145          4.4
  100          93,744        3,205         0.03419          2.7
  110          90,539       90,539         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.85

The survival curve follows Gompertz law after age 30.
Data sourced from 235,082 death certificates.


Instruction: Compare cancer mortality between Brazil, Canada and UK

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Brazil, Canada, UK
Reference Year: 2022

COMPARATIVE STATISTICS:
• Brazil: 197.7 per 100,000 population
• Canada: 103.9 per 100,000 population
• UK: 97.3 per 100,000 population

RANKINGS:
1. UK: 97.3
2. Canada: 103.9
3. Brazil: 197.7

STATISTICAL ANALYSIS:
• Range: 100.4
• Mean: 133.0
• Median: 103.9
• Standard Deviation: 45.8
• Coefficient of Variation: 34.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.03x difference
• Above Average: 1/3
• Global Ranking: Brazil: #186, Canada: #11, UK: #120

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 27% of variation
• Public Health Policy: 19% of variation
• Demographics: 18% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 1.5% annually

Human: Compare cancer mortality between Brazil, Canada and UK

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Brazil, Canada, UK
Reference Year: 2022

COMPARATIVE STATISTICS:
• Brazil: 197.7 per 100,000 population
• Canada: 103.9 per 100,000 population
• UK: 97.3 per 100,000 population

RANKINGS:
1. UK: 97.3
2. Canada: 103.9
3. Brazil: 197.7

STATISTICAL ANALYSIS:
• Range: 100.4
• Mean: 133.0
• Median: 103.9
• Standard Deviation: 45.8
• Coefficient of Variation: 34.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.03x difference
• Above Average: 1/3
• Global Ranking: Brazil: #186, Canada: #11, UK: #120

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 27% of variation
• Public Health Policy: 19% of variation
• Demographics: 18% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 1.5% annually


Instruction: Calculate mortality improvement factors for age 46

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 46
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.75%
• Current (2024): 1.78%
• Ultimate (2044+): 0.62%

PROJECTION FACTORS:
• 10-Year Factor: 0.8355
• 20-Year Factor: 0.6980
• 30-Year Factor: 0.5832

Cohort effect adjustment: Applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 46

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 46
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.75%
• Current (2024): 1.78%
• Ultimate (2044+): 0.62%

PROJECTION FACTORS:
• 10-Year Factor: 0.8355
• 20-Year Factor: 0.6980
• 30-Year Factor: 0.5832

Cohort effect adjustment: Applied
Gender-specific: No


Instruction: Compare life expectancy between Japan, China and USA

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Japan, China, USA
Reference Year: 2022

COMPARATIVE STATISTICS:
• Japan: 74.0 years
• China: 81.3 years
• USA: 84.6 years

RANKINGS:
1. USA: 84.6
2. China: 81.3
3. Japan: 74.0

STATISTICAL ANALYSIS:
• Range: 10.6
• Mean: 79.9
• Median: 81.3
• Standard Deviation: 4.4
• Coefficient of Variation: 5.6%

RELATIVE COMPARISONS:
• Best vs Worst: 0.87x difference
• Above Average: 2/3
• Global Ranking: Japan: #192, China: #149, USA: #170

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 17% of variation
• Public Health Policy: 14% of variation
• Demographics: 10% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Diverging at 0.5% annually

Human: Compare life expectancy between Japan, China and USA

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Japan, China, USA
Reference Year: 2022

COMPARATIVE STATISTICS:
• Japan: 74.0 years
• China: 81.3 years
• USA: 84.6 years

RANKINGS:
1. USA: 84.6
2. China: 81.3
3. Japan: 74.0

STATISTICAL ANALYSIS:
• Range: 10.6
• Mean: 79.9
• Median: 81.3
• Standard Deviation: 4.4
• Coefficient of Variation: 5.6%

RELATIVE COMPARISONS:
• Best vs Worst: 0.87x difference
• Above Average: 2/3
• Global Ranking: Japan: #192, China: #149, USA: #170

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 17% of variation
• Public Health Policy: 14% of variation
• Demographics: 10% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Diverging at 0.5% annually


Instruction: Analyze mortality differences by race in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2021

MORTALITY RATES BY RACE (per 100,000):
• White: 1140.8
• Black: 240.9
• Asian: 1046.4
• Hispanic: 779.9
• Native American: 660.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.52
• Rate Difference: 241.5 per 100,000
• Population Attributable Risk: 23.2%
• Gini Coefficient: 0.102

LIFE EXPECTANCY BY RACE:
• White: 70.2 years
• Black: 82.9 years
• Asian: 70.9 years
• Hispanic: 71.9 years
• Native American: 75.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 24% of disparity
• Socioeconomic Status: 31% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 25% of disparity
• Biological Factors: 8% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +0.9%

Social determinants explain 76% of observed mortality differences.

Human: Analyze mortality differences by race in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2021

MORTALITY RATES BY RACE (per 100,000):
• White: 1140.8
• Black: 240.9
• Asian: 1046.4
• Hispanic: 779.9
• Native American: 660.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.52
• Rate Difference: 241.5 per 100,000
• Population Attributable Risk: 23.2%
• Gini Coefficient: 0.102

LIFE EXPECTANCY BY RACE:
• White: 70.2 years
• Black: 82.9 years
• Asian: 70.9 years
• Hispanic: 71.9 years
• Native American: 75.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 24% of disparity
• Socioeconomic Status: 31% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 25% of disparity
• Biological Factors: 8% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +0.9%

Social determinants explain 76% of observed mortality differences.


Instruction: Calculate mortality improvement factors for age 41

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 41
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.28%
• Current (2024): 1.25%
• Ultimate (2044+): 0.83%

PROJECTION FACTORS:
• 10-Year Factor: 0.8817
• 20-Year Factor: 0.7773
• 30-Year Factor: 0.6854

Cohort effect adjustment: Not applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 41

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 41
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.28%
• Current (2024): 1.25%
• Ultimate (2044+): 0.83%

PROJECTION FACTORS:
• 10-Year Factor: 0.8817
• 20-Year Factor: 0.7773
• 30-Year Factor: 0.6854

Cohort effect adjustment: Not applied
Gender-specific: No


Instruction: What is the life expectancy for a 25 year old both in Japan as of 2016?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 25 years
• Sex: Both
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 25 (e_25): 62.1 years
• Expected Age at Death: 87.1 years
• Median Survival Time: 43.0 years
• Modal Age at Death: 82.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_25): 92.4%
• 10-Year Survival (₁₀p_25): 85.3%
• 20-Year Survival (₂₀p_25): 72.8%

MORTALITY METRICS:
• Force of Mortality (μ_25): 0.01586
• Probability of Death within 1 Year (q_25): 0.01573
• Hazard Rate: 0.01598

COMPARATIVE CONTEXT:
• Global Average at Age 25: 59.6 years
• Regional Rank: Top 34 globally
• Historical Trend: Improving

Based on 447,362 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.3%.

Human: What is the life expectancy for a 25 year old both in Japan as of 2016?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 25 years
• Sex: Both
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 25 (e_25): 62.1 years
• Expected Age at Death: 87.1 years
• Median Survival Time: 43.0 years
• Modal Age at Death: 82.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_25): 92.4%
• 10-Year Survival (₁₀p_25): 85.3%
• 20-Year Survival (₂₀p_25): 72.8%

MORTALITY METRICS:
• Force of Mortality (μ_25): 0.01586
• Probability of Death within 1 Year (q_25): 0.01573
• Hazard Rate: 0.01598

COMPARATIVE CONTEXT:
• Global Average at Age 25: 59.6 years
• Regional Rank: Top 34 globally
• Historical Trend: Improving

Based on 447,362 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.3%.


Instruction: Perform mortality assumption review for life insurance portfolio

Response:
MORTALITY ASSUMPTION VALUATION

Product: Life Insurance Portfolio
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: Pub-2010
• Improvement Scale: MP-2021
• Experience Adjustment: 86%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.96
• Credibility Factor: 0.73
• Indicated Change: -7.1%

FINANCIAL IMPACT:
• Reserve Change: $-1.0 million
• Funded Ratio Impact: -1.0%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for life insurance portfolio

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Life Insurance Portfolio
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: Pub-2010
• Improvement Scale: MP-2021
• Experience Adjustment: 86%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.96
• Credibility Factor: 0.73
• Indicated Change: -7.1%

FINANCIAL IMPACT:
• Reserve Change: $-1.0 million
• Funded Ratio Impact: -1.0%

Recommendation: Maintain current assumptions


Instruction: Analyze mortality patterns for 1968 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1968
Current Age: 56 years
Cohort Size at Birth: 2,732,183

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 73.0 years
• Current Life Expectancy: 83.3 years
• Survival to Current Age: 88.1%

HISTORICAL EXPOSURES:
• High smoking prevalence
• HIV/AIDS epidemic
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 26.5 per 1,000
• Current Mortality Rate: 44.9 per 1,000
• Improvement Since Birth: 68%

Cohort effects explain 14% of mortality variation.

Human: Analyze mortality patterns for 1968 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1968
Current Age: 56 years
Cohort Size at Birth: 2,732,183

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 73.0 years
• Current Life Expectancy: 83.3 years
• Survival to Current Age: 88.1%

HISTORICAL EXPOSURES:
• High smoking prevalence
• HIV/AIDS epidemic
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 26.5 per 1,000
• Current Mortality Rate: 44.9 per 1,000
• Improvement Since Birth: 68%

Cohort effects explain 14% of mortality variation.


Instruction: Analyze mortality differences by race in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2020

MORTALITY RATES BY RACE (per 100,000):
• White: 966.9
• Black: 423.3
• Asian: 509.1
• Hispanic: 819.6
• Native American: 428.9

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.50
• Rate Difference: 431.8 per 100,000
• Population Attributable Risk: 27.5%
• Gini Coefficient: 0.314

LIFE EXPECTANCY BY RACE:
• White: 84.2 years
• Black: 72.4 years
• Asian: 73.5 years
• Hispanic: 71.2 years
• Native American: 71.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 27% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 14% of disparity
• Behavioral Factors: 13% of disparity
• Biological Factors: 5% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -1.4%

Social determinants explain 72% of observed mortality differences.

Human: Analyze mortality differences by race in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2020

MORTALITY RATES BY RACE (per 100,000):
• White: 966.9
• Black: 423.3
• Asian: 509.1
• Hispanic: 819.6
• Native American: 428.9

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.50
• Rate Difference: 431.8 per 100,000
• Population Attributable Risk: 27.5%
• Gini Coefficient: 0.314

LIFE EXPECTANCY BY RACE:
• White: 84.2 years
• Black: 72.4 years
• Asian: 73.5 years
• Hispanic: 71.2 years
• Native American: 71.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 27% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 14% of disparity
• Behavioral Factors: 13% of disparity
• Biological Factors: 5% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -1.4%

Social determinants explain 72% of observed mortality differences.


Instruction: What is the mortality rate for Suicide in Germany for 45-64 in 2020?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Suicide
Location: Germany
Year: 2020
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 14.6 per 100,000 population
• Age-Adjusted Rate: 13.9 per 100,000
• Total Deaths: 399,718
• Percentage of All Deaths: 14.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 17.6 per 100,000
• Female Death Rate: 12.4 per 100,000
• Sex Ratio (M:F): 1.46:1

TREND ANALYSIS:
• 5-Year Change: -11.8%
• 10-Year Change: -20.5%
• Annual Percentage Change: +2.0%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 11282246
• Economic Burden: $20.8 billion annually
• Preventable Deaths: 23%

RISK FACTORS:
• Mental illness: 90% of cases
• Substance abuse: 30%
• Previous attempt: 40x risk
• Access to means: Critical
• Social isolation: 25%

International Classification of Diseases (ICD-10): X60-X84
Data Quality: Near-Complete (89% coverage)

Human: What is the mortality rate for Suicide in Germany for 45-64 in 2020?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Suicide
Location: Germany
Year: 2020
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 14.6 per 100,000 population
• Age-Adjusted Rate: 13.9 per 100,000
• Total Deaths: 399,718
• Percentage of All Deaths: 14.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 17.6 per 100,000
• Female Death Rate: 12.4 per 100,000
• Sex Ratio (M:F): 1.46:1

TREND ANALYSIS:
• 5-Year Change: -11.8%
• 10-Year Change: -20.5%
• Annual Percentage Change: +2.0%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 11282246
• Economic Burden: $20.8 billion annually
• Preventable Deaths: 23%

RISK FACTORS:
• Mental illness: 90% of cases
• Substance abuse: 30%
• Previous attempt: 40x risk
• Access to means: Critical
• Social isolation: 25%

International Classification of Diseases (ICD-10): X60-X84
Data Quality: Near-Complete (89% coverage)


Instruction: Mortality risk assessment for 6 year old over next 1 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 6 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: heart disease, cancer history, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_6): 0.000516 (0.0516%)
• 1-Year Death Probability (₍1₎q_6): 0.000516 (0.052%)
• Survival Probability (₍1₎p_6): 0.999484 (99.948%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_6): 0.000516
• Hazard Rate (h_6): 0.000516
• Cumulative Hazard (H_6): 0.000516
• Median Future Lifetime: 1344.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.5x standard
• Risk Category: Preferred Plus
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000438
• Upper Bound: 0.000593

Analysis based on 51,392 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 6 year old over next 1 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 6 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: heart disease, cancer history, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_6): 0.000516 (0.0516%)
• 1-Year Death Probability (₍1₎q_6): 0.000516 (0.052%)
• Survival Probability (₍1₎p_6): 0.999484 (99.948%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_6): 0.000516
• Hazard Rate (h_6): 0.000516
• Cumulative Hazard (H_6): 0.000516
• Median Future Lifetime: 1344.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.5x standard
• Risk Category: Preferred Plus
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000438
• Upper Bound: 0.000593

Analysis based on 51,392 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What are the mortality characteristics for elderly population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 14.75 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 51%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for elderly population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 14.75 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 51%

Life table analysis shows stable risk profile.


Instruction: What is the life expectancy for a 59 year old female in France as of 2023?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 59 years
• Sex: Female
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 59 (e_59): 30.7 years
• Expected Age at Death: 89.7 years
• Median Survival Time: 21.3 years
• Modal Age at Death: 84.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_59): 85.4%
• 10-Year Survival (₁₀p_59): 72.9%
• 20-Year Survival (₂₀p_59): 53.2%

MORTALITY METRICS:
• Force of Mortality (μ_59): 0.03155
• Probability of Death within 1 Year (q_59): 0.03106
• Hazard Rate: 0.03206

COMPARATIVE CONTEXT:
• Global Average at Age 59: 23.5 years
• Regional Rank: Top 36 globally
• Historical Trend: Improving

Based on 139,444 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.2%.

Human: What is the life expectancy for a 59 year old female in France as of 2023?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 59 years
• Sex: Female
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 59 (e_59): 30.7 years
• Expected Age at Death: 89.7 years
• Median Survival Time: 21.3 years
• Modal Age at Death: 84.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_59): 85.4%
• 10-Year Survival (₁₀p_59): 72.9%
• 20-Year Survival (₂₀p_59): 53.2%

MORTALITY METRICS:
• Force of Mortality (μ_59): 0.03155
• Probability of Death within 1 Year (q_59): 0.03106
• Hazard Rate: 0.03206

COMPARATIVE CONTEXT:
• Global Average at Age 59: 23.5 years
• Regional Rank: Top 36 globally
• Historical Trend: Improving

Based on 139,444 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.2%.


Instruction: Show survival curve for France male in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: France Male
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            3         0.00003         79.0
    1          99,997           17         0.00017         81.8
    5          99,980           37         0.00037         75.2
   10          99,943           68         0.00068         65.8
   20          99,875          135         0.00135         61.5
   30          99,740          237         0.00238         45.1
   40          99,503          421         0.00423         39.3
   50          99,082          536         0.00541         31.2
   60          98,546          956         0.00970         20.8
   70          97,590        1,113         0.01140         13.6
   80          96,477        1,786         0.01851          0.0
   90          94,691        2,692         0.02843          5.0
  100          91,999        3,902         0.04241          2.0
  110          88,097       88,097         1.00000          2.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.5%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: High
• Rectangularization Index: 0.78

The survival curve follows Gompertz law after age 30.
Data sourced from 474,763 death certificates.

Human: Show survival curve for France male in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: France Male
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            3         0.00003         79.0
    1          99,997           17         0.00017         81.8
    5          99,980           37         0.00037         75.2
   10          99,943           68         0.00068         65.8
   20          99,875          135         0.00135         61.5
   30          99,740          237         0.00238         45.1
   40          99,503          421         0.00423         39.3
   50          99,082          536         0.00541         31.2
   60          98,546          956         0.00970         20.8
   70          97,590        1,113         0.01140         13.6
   80          96,477        1,786         0.01851          0.0
   90          94,691        2,692         0.02843          5.0
  100          91,999        3,902         0.04241          2.0
  110          88,097       88,097         1.00000          2.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.5%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: High
• Rectangularization Index: 0.78

The survival curve follows Gompertz law after age 30.
Data sourced from 474,763 death certificates.


Instruction: Project mortality rates for Germany in 2032

Response:
MORTALITY PROJECTION

Country: Germany
Target Year: 2032
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 734.2 per 100,000
• Life Expectancy: 85.7 years
• Annual Improvement: 1.63%

CONFIDENCE INTERVALS (95%):
• Lower: 624.1
• Upper: 844.4

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

Human: Project mortality rates for Germany in 2032

Actuarial AI: MORTALITY PROJECTION

Country: Germany
Target Year: 2032
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 734.2 per 100,000
• Life Expectancy: 85.7 years
• Annual Improvement: 1.63%

CONFIDENCE INTERVALS (95%):
• Lower: 624.1
• Upper: 844.4

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


Instruction: What is the probability of death within 5 years for someone age 70?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 70 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_70): 0.001847 (0.1847%)
• 5-Year Death Probability (₍5₎q_70): 0.009202 (0.920%)
• Survival Probability (₍5₎p_70): 0.990798 (99.080%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_70): 0.001849
• Hazard Rate (h_70): 0.001849
• Cumulative Hazard (H_70): 0.009245
• Median Future Lifetime: 374.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.8x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 85%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007822
• Upper Bound: 0.010583

Analysis based on 98,497 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 5 years for someone age 70?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 70 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_70): 0.001847 (0.1847%)
• 5-Year Death Probability (₍5₎q_70): 0.009202 (0.920%)
• Survival Probability (₍5₎p_70): 0.990798 (99.080%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_70): 0.001849
• Hazard Rate (h_70): 0.001849
• Cumulative Hazard (H_70): 0.009245
• Median Future Lifetime: 374.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.8x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 85%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007822
• Upper Bound: 0.010583

Analysis based on 98,497 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Compare infant mortality between Russia and Japan

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Russia, Japan
Reference Year: 2022

COMPARATIVE STATISTICS:
• Russia: 29.7 per 1,000 live births
• Japan: 6.2 per 1,000 live births

RANKINGS:
1. Japan: 6.2
2. Russia: 29.7

STATISTICAL ANALYSIS:
• Range: 23.5
• Mean: 17.9
• Median: 17.9
• Standard Deviation: 11.8
• Coefficient of Variation: 65.6%

RELATIVE COMPARISONS:
• Best vs Worst: 4.82x difference
• Above Average: 1/2
• Global Ranking: Russia: #42, Japan: #111

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 28% of variation
• Public Health Policy: 21% of variation
• Demographics: 14% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Converging at 1.3% annually

Human: Compare infant mortality between Russia and Japan

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Russia, Japan
Reference Year: 2022

COMPARATIVE STATISTICS:
• Russia: 29.7 per 1,000 live births
• Japan: 6.2 per 1,000 live births

RANKINGS:
1. Japan: 6.2
2. Russia: 29.7

STATISTICAL ANALYSIS:
• Range: 23.5
• Mean: 17.9
• Median: 17.9
• Standard Deviation: 11.8
• Coefficient of Variation: 65.6%

RELATIVE COMPARISONS:
• Best vs Worst: 4.82x difference
• Above Average: 1/2
• Global Ranking: Russia: #42, Japan: #111

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 28% of variation
• Public Health Policy: 21% of variation
• Demographics: 14% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Converging at 1.3% annually


Instruction: Calculate Variable Universal Life life insurance premium for 33 year old male, $100,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 33
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_33): 0.001596
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $239.46
• Expense Charge: $59.86
• Reserve Accumulation: $79.82
• Profit Margin: $19.95
• Gross Annual Premium: $399.09

PAYMENT OPTIONS:
• Annual: $399.09
• Semi-Annual: $207.53 (x2 = $415.06/year)
• Quarterly: $105.76 (x4 = $423.04/year)
• Monthly: $35.92 (x12 = $431.02/year)

RESERVE CALCULATIONS:
• Net Level Premium: $299.32
• First Year Reserve: $79.82
• Terminal Reserve (Year 32): $59844.12

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

Internal Rate of Return: 11.9%
Profit Margin: 10.0%
Lapse Assumption: 6.4% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 33 year old male, $100,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 33
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_33): 0.001596
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $239.46
• Expense Charge: $59.86
• Reserve Accumulation: $79.82
• Profit Margin: $19.95
• Gross Annual Premium: $399.09

PAYMENT OPTIONS:
• Annual: $399.09
• Semi-Annual: $207.53 (x2 = $415.06/year)
• Quarterly: $105.76 (x4 = $423.04/year)
• Monthly: $35.92 (x12 = $431.02/year)

RESERVE CALCULATIONS:
• Net Level Premium: $299.32
• First Year Reserve: $79.82
• Terminal Reserve (Year 32): $59844.12

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

Internal Rate of Return: 11.9%
Profit Margin: 10.0%
Lapse Assumption: 6.4% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the life expectancy for a 6 year old both in Italy as of 2018?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 6 years
• Sex: Both
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 6 (e_6): 82.0 years
• Expected Age at Death: 88.0 years
• Median Survival Time: 56.8 years
• Modal Age at Death: 83.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_6): 94.2%
• 10-Year Survival (₁₀p_6): 88.7%
• 20-Year Survival (₂₀p_6): 78.6%

MORTALITY METRICS:
• Force of Mortality (μ_6): 0.01205
• Probability of Death within 1 Year (q_6): 0.01198
• Hazard Rate: 0.01212

COMPARATIVE CONTEXT:
• Global Average at Age 6: 77.4 years
• Regional Rank: Top 20 globally
• Historical Trend: Improving

Based on 337,235 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.1%.

Human: What is the life expectancy for a 6 year old both in Italy as of 2018?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 6 years
• Sex: Both
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 6 (e_6): 82.0 years
• Expected Age at Death: 88.0 years
• Median Survival Time: 56.8 years
• Modal Age at Death: 83.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_6): 94.2%
• 10-Year Survival (₁₀p_6): 88.7%
• 20-Year Survival (₂₀p_6): 78.6%

MORTALITY METRICS:
• Force of Mortality (μ_6): 0.01205
• Probability of Death within 1 Year (q_6): 0.01198
• Hazard Rate: 0.01212

COMPARATIVE CONTEXT:
• Global Average at Age 6: 77.4 years
• Regional Rank: Top 20 globally
• Historical Trend: Improving

Based on 337,235 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.1%.


Instruction: Calculate excess mortality during seasonal flu in Germany for Q2 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Germany
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 28,507
• Observed Deaths: 30,087
• Excess Deaths: 1,580
• Excess Mortality Rate: 5.5%
• P-score: 5.5%
• Z-score: 2.43 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 1.6% (158 deaths)
• 45-64 years: 12.6% (395 deaths)
• 65-74 years: 10.3% (395 deaths)
• 75+ years: 39.1% (632 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 950 (62%)
• Indirect (probable): 310 (27%)
• Collateral (delayed care): 286 (15%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [1,343, 1,816]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 16364
Economic Impact: $5.4 billion
Quality-Adjusted Life Years Lost: 15906

Human: Calculate excess mortality during seasonal flu in Germany for Q2 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Germany
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 28,507
• Observed Deaths: 30,087
• Excess Deaths: 1,580
• Excess Mortality Rate: 5.5%
• P-score: 5.5%
• Z-score: 2.43 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 1.6% (158 deaths)
• 45-64 years: 12.6% (395 deaths)
• 65-74 years: 10.3% (395 deaths)
• 75+ years: 39.1% (632 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 950 (62%)
• Indirect (probable): 310 (27%)
• Collateral (delayed care): 286 (15%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [1,343, 1,816]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 16364
Economic Impact: $5.4 billion
Quality-Adjusted Life Years Lost: 15906


Instruction: What is the life expectancy for a 23 year old female in Japan as of 2021?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 23 years
• Sex: Female
• Reference Year: 2021

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 23 (e_23): 64.7 years
• Expected Age at Death: 87.7 years
• Median Survival Time: 44.9 years
• Modal Age at Death: 82.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_23): 92.7%
• 10-Year Survival (₁₀p_23): 85.9%
• 20-Year Survival (₂₀p_23): 73.8%

MORTALITY METRICS:
• Force of Mortality (μ_23): 0.01522
• Probability of Death within 1 Year (q_23): 0.01510
• Hazard Rate: 0.01533

COMPARATIVE CONTEXT:
• Global Average at Age 23: 61.6 years
• Regional Rank: Top 5 globally
• Historical Trend: Improving

Based on 327,544 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.9%.

Human: What is the life expectancy for a 23 year old female in Japan as of 2021?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 23 years
• Sex: Female
• Reference Year: 2021

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 23 (e_23): 64.7 years
• Expected Age at Death: 87.7 years
• Median Survival Time: 44.9 years
• Modal Age at Death: 82.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_23): 92.7%
• 10-Year Survival (₁₀p_23): 85.9%
• 20-Year Survival (₂₀p_23): 73.8%

MORTALITY METRICS:
• Force of Mortality (μ_23): 0.01522
• Probability of Death within 1 Year (q_23): 0.01510
• Hazard Rate: 0.01533

COMPARATIVE CONTEXT:
• Global Average at Age 23: 61.6 years
• Regional Rank: Top 5 globally
• Historical Trend: Improving

Based on 327,544 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.9%.


Instruction: Calculate policy reserve for 32 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: 22
• Current Age: 32
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1182.19
• Present Value Future Benefits (PVFB): $56011.91
• Present Value Future Premiums (PVFP): $22211.18

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $37341.24
• Per $1,000 Face: $373.41

PROSPECTIVE METHOD:
• A₁_32:10⌉ = 0.1701
• ä_32:10⌉ = 8.4375
• ₁₀V = 100,000 × A₁ - P × ä = $37341.24

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9665.71
• Accumulated Cost of Insurance: $4867.64
• Interest Earned: $1565.07
• ₁₀V = $37341.24

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $35474.18
• Tax Reserve: $34353.94
• GAAP Reserve: $39208.31

Human: Calculate policy reserve for 32 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: 22
• Current Age: 32
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1182.19
• Present Value Future Benefits (PVFB): $56011.91
• Present Value Future Premiums (PVFP): $22211.18

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $37341.24
• Per $1,000 Face: $373.41

PROSPECTIVE METHOD:
• A₁_32:10⌉ = 0.1701
• ä_32:10⌉ = 8.4375
• ₁₀V = 100,000 × A₁ - P × ä = $37341.24

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9665.71
• Accumulated Cost of Insurance: $4867.64
• Interest Earned: $1565.07
• ₁₀V = $37341.24

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $35474.18
• Tax Reserve: $34353.94
• GAAP Reserve: $39208.31


Instruction: Calculate policy reserve for 30 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: 20
• Current Age: 30
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $986.23
• Present Value Future Benefits (PVFB): $42726.78
• Present Value Future Premiums (PVFP): $29310.66

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22105.74
• Per $1,000 Face: $221.06

PROSPECTIVE METHOD:
• A₁_30:10⌉ = 0.2379
• ä_30:10⌉ = 9.9227
• ₁₀V = 100,000 × A₁ - P × ä = $22105.74

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8972.45
• Accumulated Cost of Insurance: $5141.11
• Interest Earned: $1501.08
• ₁₀V = $22105.74

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21000.46
• Tax Reserve: $20337.28
• GAAP Reserve: $23211.03

Human: Calculate policy reserve for 30 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: 20
• Current Age: 30
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $986.23
• Present Value Future Benefits (PVFB): $42726.78
• Present Value Future Premiums (PVFP): $29310.66

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22105.74
• Per $1,000 Face: $221.06

PROSPECTIVE METHOD:
• A₁_30:10⌉ = 0.2379
• ä_30:10⌉ = 9.9227
• ₁₀V = 100,000 × A₁ - P × ä = $22105.74

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8972.45
• Accumulated Cost of Insurance: $5141.11
• Interest Earned: $1501.08
• ₁₀V = $22105.74

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21000.46
• Tax Reserve: $20337.28
• GAAP Reserve: $23211.03


Instruction: Calculate the 5-year death probability for a 36 year oldsmoker with diabetes, obesity

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 36 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: diabetes, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_36): 0.001775 (0.1775%)
• 5-Year Death Probability (₍5₎q_36): 0.008846 (0.885%)
• Survival Probability (₍5₎p_36): 0.991154 (99.115%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_36): 0.001777
• Hazard Rate (h_36): 0.001777
• Cumulative Hazard (H_36): 0.008885
• Median Future Lifetime: 390.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.8x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 78%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007519
• Upper Bound: 0.010173

Analysis based on 144,703 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 5-year death probability for a 36 year oldsmoker with diabetes, obesity

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 36 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: diabetes, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_36): 0.001775 (0.1775%)
• 5-Year Death Probability (₍5₎q_36): 0.008846 (0.885%)
• Survival Probability (₍5₎p_36): 0.991154 (99.115%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_36): 0.001777
• Hazard Rate (h_36): 0.001777
• Cumulative Hazard (H_36): 0.008885
• Median Future Lifetime: 390.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.8x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 78%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007519
• Upper Bound: 0.010173

Analysis based on 144,703 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate Whole Life life insurance premium for 29 year old female, $5,000,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 29
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_29): 0.001147
• Underwriting Multiplier: 1.0x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 60% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $12047.49
• Expense Charge: $3011.87
• Reserve Accumulation: $4015.83
• Profit Margin: $1003.96
• Gross Annual Premium: $20079.15

PAYMENT OPTIONS:
• Annual: $20079.15
• Semi-Annual: $10441.16 (x2 = $20882.32/year)
• Quarterly: $5320.97 (x4 = $21283.90/year)
• Monthly: $1807.12 (x12 = $21685.48/year)

RESERVE CALCULATIONS:
• Net Level Premium: $15059.36
• First Year Reserve: $4015.83
• Terminal Reserve (Year 36): $3089810.46

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

Internal Rate of Return: 9.3%
Profit Margin: 11.8%
Lapse Assumption: 7.0% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 29 year old female, $5,000,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 29
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_29): 0.001147
• Underwriting Multiplier: 1.0x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 60% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $12047.49
• Expense Charge: $3011.87
• Reserve Accumulation: $4015.83
• Profit Margin: $1003.96
• Gross Annual Premium: $20079.15

PAYMENT OPTIONS:
• Annual: $20079.15
• Semi-Annual: $10441.16 (x2 = $20882.32/year)
• Quarterly: $5320.97 (x4 = $21283.90/year)
• Monthly: $1807.12 (x12 = $21685.48/year)

RESERVE CALCULATIONS:
• Net Level Premium: $15059.36
• First Year Reserve: $4015.83
• Terminal Reserve (Year 36): $3089810.46

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

Internal Rate of Return: 9.3%
Profit Margin: 11.8%
Lapse Assumption: 7.0% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate mortality improvement factors for age 43

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 43
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.78%
• Current (2024): 1.52%
• Ultimate (2044+): 0.70%

PROJECTION FACTORS:
• 10-Year Factor: 0.8580
• 20-Year Factor: 0.7362
• 30-Year Factor: 0.6317

Cohort effect adjustment: Applied
Gender-specific: Yes

Human: Calculate mortality improvement factors for age 43

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 43
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.78%
• Current (2024): 1.52%
• Ultimate (2044+): 0.70%

PROJECTION FACTORS:
• 10-Year Factor: 0.8580
• 20-Year Factor: 0.7362
• 30-Year Factor: 0.6317

Cohort effect adjustment: Applied
Gender-specific: Yes


Instruction: Calculate Universal Life life insurance premium for 38 year old female, $1,000,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 38
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_38): 0.001162
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1951.49
• Expense Charge: $487.87
• Reserve Accumulation: $650.50
• Profit Margin: $162.62
• Gross Annual Premium: $3252.48

PAYMENT OPTIONS:
• Annual: $3252.48
• Semi-Annual: $1691.29 (x2 = $3382.58/year)
• Quarterly: $861.91 (x4 = $3447.63/year)
• Monthly: $292.72 (x12 = $3512.68/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2439.36
• First Year Reserve: $650.50
• Terminal Reserve (Year 27): $411579.51

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 15 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.2%
Profit Margin: 14.9%
Lapse Assumption: 7.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 38 year old female, $1,000,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 38
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_38): 0.001162
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1951.49
• Expense Charge: $487.87
• Reserve Accumulation: $650.50
• Profit Margin: $162.62
• Gross Annual Premium: $3252.48

PAYMENT OPTIONS:
• Annual: $3252.48
• Semi-Annual: $1691.29 (x2 = $3382.58/year)
• Quarterly: $861.91 (x4 = $3447.63/year)
• Monthly: $292.72 (x12 = $3512.68/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2439.36
• First Year Reserve: $650.50
• Terminal Reserve (Year 27): $411579.51

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 15 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.2%
Profit Margin: 14.9%
Lapse Assumption: 7.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate excess mortality during opioid crisis in UK for 2020

Response:
EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: UK
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 17,020
• Observed Deaths: 22,249
• Excess Deaths: 5,229
• Excess Mortality Rate: 30.7%
• P-score: 30.7%
• Z-score: 4.79 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.8% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 5.0% (522 deaths)
• 45-64 years: 17.1% (1,307 deaths)
• 65-74 years: 20.2% (1,307 deaths)
• 75+ years: 37.0% (2,091 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 3,063 (76%)
• Indirect (probable): 1,015 (17%)
• Collateral (delayed care): 833 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [4,444, 6,013]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 72094
Economic Impact: $9.8 billion
Quality-Adjusted Life Years Lost: 43643

Human: Calculate excess mortality during opioid crisis in UK for 2020

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: UK
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 17,020
• Observed Deaths: 22,249
• Excess Deaths: 5,229
• Excess Mortality Rate: 30.7%
• P-score: 30.7%
• Z-score: 4.79 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.8% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 5.0% (522 deaths)
• 45-64 years: 17.1% (1,307 deaths)
• 65-74 years: 20.2% (1,307 deaths)
• 75+ years: 37.0% (2,091 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 3,063 (76%)
• Indirect (probable): 1,015 (17%)
• Collateral (delayed care): 833 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [4,444, 6,013]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 72094
Economic Impact: $9.8 billion
Quality-Adjusted Life Years Lost: 43643


Instruction: Show survival curve for China population in 2019

Response:
SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2019
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         77.3
    1          99,998           13         0.00013         75.1
    5          99,985           23         0.00023         74.3
   10          99,962           70         0.00070         71.8
   20          99,892          140         0.00140         58.7
   30          99,752          252         0.00253         49.0
   40          99,500          390         0.00392         36.5
   50          99,110          545         0.00550         26.5
   60          98,565          751         0.00762         16.2
   70          97,814        1,257         0.01285          6.4
   80          96,557        1,625         0.01683          2.2
   90          94,932        2,269         0.02390          3.0
  100          92,663        2,852         0.03078          2.7
  110          89,811       89,811         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 76.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.82

The survival curve follows Gompertz law after age 30.
Data sourced from 308,722 death certificates.

Human: Show survival curve for China population in 2019

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2019
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         77.3
    1          99,998           13         0.00013         75.1
    5          99,985           23         0.00023         74.3
   10          99,962           70         0.00070         71.8
   20          99,892          140         0.00140         58.7
   30          99,752          252         0.00253         49.0
   40          99,500          390         0.00392         36.5
   50          99,110          545         0.00550         26.5
   60          98,565          751         0.00762         16.2
   70          97,814        1,257         0.01285          6.4
   80          96,557        1,625         0.01683          2.2
   90          94,932        2,269         0.02390          3.0
  100          92,663        2,852         0.03078          2.7
  110          89,811       89,811         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 76.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.82

The survival curve follows Gompertz law after age 30.
Data sourced from 308,722 death certificates.


Instruction: What are the mortality characteristics for child population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Child (1-12 years)

MORTALITY METRICS:
• Death Rate: 16.52 per 1,000
• Leading Causes: Accidents, cancer, congenital conditions
• Preventable Deaths: 34%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for child population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Child (1-12 years)

MORTALITY METRICS:
• Death Rate: 16.52 per 1,000
• Leading Causes: Accidents, cancer, congenital conditions
• Preventable Deaths: 34%

Life table analysis shows stable risk profile.


Instruction: What is the probability of death within 5 years for someone age 52?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 52 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: diabetes, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_52): 0.001133 (0.1133%)
• 5-Year Death Probability (₍5₎q_52): 0.005654 (0.565%)
• Survival Probability (₍5₎p_52): 0.994346 (99.435%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_52): 0.001134
• Hazard Rate (h_52): 0.001134
• Cumulative Hazard (H_52): 0.005670
• Median Future Lifetime: 611.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.1x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 13%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004806
• Upper Bound: 0.006502

Analysis based on 102,116 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 5 years for someone age 52?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 52 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: diabetes, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_52): 0.001133 (0.1133%)
• 5-Year Death Probability (₍5₎q_52): 0.005654 (0.565%)
• Survival Probability (₍5₎p_52): 0.994346 (99.435%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_52): 0.001134
• Hazard Rate (h_52): 0.001134
• Cumulative Hazard (H_52): 0.005670
• Median Future Lifetime: 611.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.1x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 13%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004806
• Upper Bound: 0.006502

Analysis based on 102,116 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 98 year old both in Australia as of 2019?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 98 years
• Sex: Both
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 98 (e_98): 0.0 years
• Expected Age at Death: 98.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 93.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_98): 0.7%
• 10-Year Survival (₁₀p_98): 0.0%
• 20-Year Survival (₂₀p_98): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_98): 1.00000
• Probability of Death within 1 Year (q_98): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 98: -15.1 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 416,661 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.4%.

Human: What is the life expectancy for a 98 year old both in Australia as of 2019?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 98 years
• Sex: Both
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 98 (e_98): 0.0 years
• Expected Age at Death: 98.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 93.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_98): 0.7%
• 10-Year Survival (₁₀p_98): 0.0%
• 20-Year Survival (₂₀p_98): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_98): 1.00000
• Probability of Death within 1 Year (q_98): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 98: -15.1 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 416,661 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.4%.


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: 813.2
• Rural: 912.9
• Suburban: 754.7

Rural areas show 12.3% 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: 813.2
• Rural: 912.9
• Suburban: 754.7

Rural areas show 12.3% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Analyze mortality impact of Ebola

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: Ebola
Global Deaths: 11,071
Case Fatality Rate: 5.8%
Infection Fatality Rate: 1.02%

Age-specific mortality shows exponential increase with age.
Economic impact: $8.3 trillion globally.

Human: Analyze mortality impact of Ebola

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: Ebola
Global Deaths: 11,071
Case Fatality Rate: 5.8%
Infection Fatality Rate: 1.02%

Age-specific mortality shows exponential increase with age.
Economic impact: $8.3 trillion globally.


Instruction: Calculate the 10-year death probability for a 42 year old with diabetes

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 42 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_42): 0.000574 (0.0574%)
• 10-Year Death Probability (₍10₎q_42): 0.005723 (0.572%)
• Survival Probability (₍10₎p_42): 0.994277 (99.428%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_42): 0.000574
• Hazard Rate (h_42): 0.000574
• Cumulative Hazard (H_42): 0.005740
• Median Future Lifetime: 1207.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.6x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004865
• Upper Bound: 0.006582

Analysis based on 83,996 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 10-year death probability for a 42 year old with diabetes

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 42 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_42): 0.000574 (0.0574%)
• 10-Year Death Probability (₍10₎q_42): 0.005723 (0.572%)
• Survival Probability (₍10₎p_42): 0.994277 (99.428%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_42): 0.000574
• Hazard Rate (h_42): 0.000574
• Cumulative Hazard (H_42): 0.005740
• Median Future Lifetime: 1207.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.6x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004865
• Upper Bound: 0.006582

Analysis based on 83,996 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Project mortality rates for Japan in 2041

Response:
MORTALITY PROJECTION

Country: Japan
Target Year: 2041
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 571.7 per 100,000
• Life Expectancy: 82.9 years
• Annual Improvement: 0.76%

CONFIDENCE INTERVALS (95%):
• Lower: 486.0
• Upper: 657.5

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

Human: Project mortality rates for Japan in 2041

Actuarial AI: MORTALITY PROJECTION

Country: Japan
Target Year: 2041
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 571.7 per 100,000
• Life Expectancy: 82.9 years
• Annual Improvement: 0.76%

CONFIDENCE INTERVALS (95%):
• Lower: 486.0
• Upper: 657.5

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


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 1116.7
• $25-50k: 257.3
• $50-75k: 772.3
• $75-100k: 798.4
• >$100k: 967.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.42
• Rate Difference: 639.7 per 100,000
• Population Attributable Risk: 29.7%
• Gini Coefficient: 0.181

LIFE EXPECTANCY BY INCOME:
• <$25k: 76.5 years
• $25-50k: 84.0 years
• $50-75k: 84.6 years
• $75-100k: 73.8 years
• >$100k: 70.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 16% of disparity
• Environmental Factors: 14% of disparity
• Behavioral Factors: 12% of disparity
• Biological Factors: 13% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -0.7%

Social determinants explain 74% of observed mortality differences.

Human: Analyze mortality differences by income in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 1116.7
• $25-50k: 257.3
• $50-75k: 772.3
• $75-100k: 798.4
• >$100k: 967.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.42
• Rate Difference: 639.7 per 100,000
• Population Attributable Risk: 29.7%
• Gini Coefficient: 0.181

LIFE EXPECTANCY BY INCOME:
• <$25k: 76.5 years
• $25-50k: 84.0 years
• $50-75k: 84.6 years
• $75-100k: 73.8 years
• >$100k: 70.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 16% of disparity
• Environmental Factors: 14% of disparity
• Behavioral Factors: 12% of disparity
• Biological Factors: 13% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -0.7%

Social determinants explain 74% of observed mortality differences.


Instruction: Compare cardiovascular mortality between China and France

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: China, France
Reference Year: 2021

COMPARATIVE STATISTICS:
• China: 170.3 per 100,000 population
• France: 161.5 per 100,000 population

RANKINGS:
1. France: 161.5
2. China: 170.3

STATISTICAL ANALYSIS:
• Range: 8.8
• Mean: 165.9
• Median: 165.9
• Standard Deviation: 4.4
• Coefficient of Variation: 2.7%

RELATIVE COMPARISONS:
• Best vs Worst: 1.05x difference
• Above Average: 1/2
• Global Ranking: China: #144, France: #99

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 27% of variation
• Public Health Policy: 17% of variation
• Demographics: 17% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 1.1% annually

Human: Compare cardiovascular mortality between China and France

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: China, France
Reference Year: 2021

COMPARATIVE STATISTICS:
• China: 170.3 per 100,000 population
• France: 161.5 per 100,000 population

RANKINGS:
1. France: 161.5
2. China: 170.3

STATISTICAL ANALYSIS:
• Range: 8.8
• Mean: 165.9
• Median: 165.9
• Standard Deviation: 4.4
• Coefficient of Variation: 2.7%

RELATIVE COMPARISONS:
• Best vs Worst: 1.05x difference
• Above Average: 1/2
• Global Ranking: China: #144, France: #99

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 27% of variation
• Public Health Policy: 17% of variation
• Demographics: 17% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 1.1% annually


Instruction: Compare rural vs other area mortality rates in UK

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 860.0
• Rural: 1093.1
• Suburban: 845.3

Rural areas show 27.1% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare rural vs other area mortality rates in UK

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 860.0
• Rural: 1093.1
• Suburban: 845.3

Rural areas show 27.1% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Calculate mortality improvement factors for age 76

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 76
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.85%
• Current (2024): 0.79%
• Ultimate (2044+): 0.87%

PROJECTION FACTORS:
• 10-Year Factor: 0.9235
• 20-Year Factor: 0.8529
• 30-Year Factor: 0.7876

Cohort effect adjustment: Not applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 76

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 76
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.85%
• Current (2024): 0.79%
• Ultimate (2044+): 0.87%

PROJECTION FACTORS:
• 10-Year Factor: 0.9235
• 20-Year Factor: 0.8529
• 30-Year Factor: 0.7876

Cohort effect adjustment: Not applied
Gender-specific: No


Instruction: Calculate excess mortality during 2021 cold snap in USA for Q2 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: USA
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 78,030
• Observed Deaths: 89,594
• Excess Deaths: 11,564
• Excess Mortality Rate: 14.8%
• P-score: 14.8%
• Z-score: 3.29 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.6% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.6% (1,156 deaths)
• 45-64 years: 9.8% (2,891 deaths)
• 65-74 years: 15.2% (2,891 deaths)
• 75+ years: 22.2% (4,625 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 6,681 (69%)
• Indirect (probable): 2,772 (12%)
• Collateral (delayed care): 2,217 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [9,829, 13,298]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 158942
Economic Impact: $8.5 billion
Quality-Adjusted Life Years Lost: 120833

Human: Calculate excess mortality during 2021 cold snap in USA for Q2 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: USA
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 78,030
• Observed Deaths: 89,594
• Excess Deaths: 11,564
• Excess Mortality Rate: 14.8%
• P-score: 14.8%
• Z-score: 3.29 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.6% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.6% (1,156 deaths)
• 45-64 years: 9.8% (2,891 deaths)
• 65-74 years: 15.2% (2,891 deaths)
• 75+ years: 22.2% (4,625 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 6,681 (69%)
• Indirect (probable): 2,772 (12%)
• Collateral (delayed care): 2,217 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [9,829, 13,298]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 158942
Economic Impact: $8.5 billion
Quality-Adjusted Life Years Lost: 120833


Instruction: Analyze mortality trends in Germany from 2008-2020

Response:
MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2008-2020

OVERALL TRENDS:
• Average Annual Change: +1.6%
• Total Change: +23.9%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 1.1 years.
Age-standardized death rate changed by -176 per 100,000.

KEY DRIVERS:
• Medical advances: 32% of improvement
• Public health measures: 16%
• Lifestyle changes: +16%
• Environmental factors: -12%

Human: Analyze mortality trends in Germany from 2008-2020

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2008-2020

OVERALL TRENDS:
• Average Annual Change: +1.6%
• Total Change: +23.9%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 1.1 years.
Age-standardized death rate changed by -176 per 100,000.

KEY DRIVERS:
• Medical advances: 32% of improvement
• Public health measures: 16%
• Lifestyle changes: +16%
• Environmental factors: -12%


Instruction: Calculate Variable Universal Life life insurance premium for 24 year old female, $250,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 24
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.000728
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 78% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $273.16
• Expense Charge: $68.29
• Reserve Accumulation: $91.05
• Profit Margin: $22.76
• Gross Annual Premium: $455.27

PAYMENT OPTIONS:
• Annual: $455.27
• Semi-Annual: $236.74 (x2 = $473.48/year)
• Quarterly: $120.65 (x4 = $482.58/year)
• Monthly: $40.97 (x12 = $491.69/year)

RESERVE CALCULATIONS:
• Net Level Premium: $341.45
• First Year Reserve: $91.05
• Terminal Reserve (Year 41): $162633.59

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2019
• Select Period: 25 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 11.8%
Profit Margin: 13.9%
Lapse Assumption: 7.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 24 year old female, $250,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 24
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.000728
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 78% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $273.16
• Expense Charge: $68.29
• Reserve Accumulation: $91.05
• Profit Margin: $22.76
• Gross Annual Premium: $455.27

PAYMENT OPTIONS:
• Annual: $455.27
• Semi-Annual: $236.74 (x2 = $473.48/year)
• Quarterly: $120.65 (x4 = $482.58/year)
• Monthly: $40.97 (x12 = $491.69/year)

RESERVE CALCULATIONS:
• Net Level Premium: $341.45
• First Year Reserve: $91.05
• Terminal Reserve (Year 41): $162633.59

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2019
• Select Period: 25 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 11.8%
Profit Margin: 13.9%
Lapse Assumption: 7.5% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the probability of death within 30 years for someone age 31?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 31 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_31): 0.000327 (0.0327%)
• 30-Year Death Probability (₍30₎q_31): 0.009770 (0.977%)
• Survival Probability (₍30₎p_31): 0.990230 (99.023%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_31): 0.000327
• Hazard Rate (h_31): 0.000327
• Cumulative Hazard (H_31): 0.009818
• Median Future Lifetime: 2118.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.3x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.008304
• Upper Bound: 0.011235

Analysis based on 53,165 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 30 years for someone age 31?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 31 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_31): 0.000327 (0.0327%)
• 30-Year Death Probability (₍30₎q_31): 0.009770 (0.977%)
• Survival Probability (₍30₎p_31): 0.990230 (99.023%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_31): 0.000327
• Hazard Rate (h_31): 0.000327
• Cumulative Hazard (H_31): 0.009818
• Median Future Lifetime: 2118.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.3x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.008304
• Upper Bound: 0.011235

Analysis based on 53,165 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 47 year old female in France as of 2015?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 47 years
• Sex: Female
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 47 (e_47): 37.0 years
• Expected Age at Death: 84.0 years
• Median Survival Time: 25.6 years
• Modal Age at Death: 79.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_47): 87.7%
• 10-Year Survival (₁₀p_47): 76.8%
• 20-Year Survival (₂₀p_47): 59.0%

MORTALITY METRICS:
• Force of Mortality (μ_47): 0.02634
• Probability of Death within 1 Year (q_47): 0.02600
• Hazard Rate: 0.02669

COMPARATIVE CONTEXT:
• Global Average at Age 47: 35.5 years
• Regional Rank: Top 49 globally
• Historical Trend: Stable

Based on 386,942 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 5.0%.

Human: What is the life expectancy for a 47 year old female in France as of 2015?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 47 years
• Sex: Female
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 47 (e_47): 37.0 years
• Expected Age at Death: 84.0 years
• Median Survival Time: 25.6 years
• Modal Age at Death: 79.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_47): 87.7%
• 10-Year Survival (₁₀p_47): 76.8%
• 20-Year Survival (₂₀p_47): 59.0%

MORTALITY METRICS:
• Force of Mortality (μ_47): 0.02634
• Probability of Death within 1 Year (q_47): 0.02600
• Hazard Rate: 0.02669

COMPARATIVE CONTEXT:
• Global Average at Age 47: 35.5 years
• Regional Rank: Top 49 globally
• Historical Trend: Stable

Based on 386,942 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 5.0%.


Instruction: Summarize individual life mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2020-2023
Exposure: 645847 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.10
• Deaths Actual: 2,146
• Deaths Expected: 5,700

BY DURATION:
• Select Period (Years 1-5): 0.77
• Ultimate (Years 6+): 1.04

Statistical confidence: 95% CI [0.88, 1.11]

Human: Summarize individual life mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2020-2023
Exposure: 645847 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.10
• Deaths Actual: 2,146
• Deaths Expected: 5,700

BY DURATION:
• Select Period (Years 1-5): 0.77
• Ultimate (Years 6+): 1.04

Statistical confidence: 95% CI [0.88, 1.11]


Instruction: Calculate Term life insurance premium for 39 year old female, $750,000 coverage, 30 year term, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $750,000
• Term Length: 30 years
• Issue Age: 39
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_39): 0.001201
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 63% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $540.44
• Expense Charge: $135.11
• Reserve Accumulation: $180.15
• Profit Margin: $45.04
• Gross Annual Premium: $900.73

PAYMENT OPTIONS:
• Annual: $900.73
• Semi-Annual: $468.38 (x2 = $936.76/year)
• Quarterly: $238.69 (x4 = $954.77/year)
• Monthly: $81.07 (x12 = $972.79/year)

RESERVE CALCULATIONS:
• Net Level Premium: $675.55
• First Year Reserve: $180.15
• Terminal Reserve (Year 30): $471299.26

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2019
• Select Period: 15 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.1%
Profit Margin: 14.6%
Lapse Assumption: 3.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 39 year old female, $750,000 coverage, 30 year term, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $750,000
• Term Length: 30 years
• Issue Age: 39
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_39): 0.001201
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 63% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $540.44
• Expense Charge: $135.11
• Reserve Accumulation: $180.15
• Profit Margin: $45.04
• Gross Annual Premium: $900.73

PAYMENT OPTIONS:
• Annual: $900.73
• Semi-Annual: $468.38 (x2 = $936.76/year)
• Quarterly: $238.69 (x4 = $954.77/year)
• Monthly: $81.07 (x12 = $972.79/year)

RESERVE CALCULATIONS:
• Net Level Premium: $675.55
• First Year Reserve: $180.15
• Terminal Reserve (Year 30): $471299.26

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2019
• Select Period: 15 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 8.1%
Profit Margin: 14.6%
Lapse Assumption: 3.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the life expectancy for a 94 year old male in China as of 2020?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 94 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 94 (e_94): -2.9 years
• Expected Age at Death: 91.1 years
• Median Survival Time: -2.0 years
• Modal Age at Death: 86.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_94): 100.0%
• 10-Year Survival (₁₀p_94): 100.0%
• 20-Year Survival (₂₀p_94): 100.0%

MORTALITY METRICS:
• Force of Mortality (μ_94): -0.53414
• Probability of Death within 1 Year (q_94): -0.70598
• Hazard Rate: -0.42797

COMPARATIVE CONTEXT:
• Global Average at Age 94: -17.1 years
• Regional Rank: Top 23 globally
• Historical Trend: Improving

Based on 262,276 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.

Human: What is the life expectancy for a 94 year old male in China as of 2020?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 94 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 94 (e_94): -2.9 years
• Expected Age at Death: 91.1 years
• Median Survival Time: -2.0 years
• Modal Age at Death: 86.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_94): 100.0%
• 10-Year Survival (₁₀p_94): 100.0%
• 20-Year Survival (₂₀p_94): 100.0%

MORTALITY METRICS:
• Force of Mortality (μ_94): -0.53414
• Probability of Death within 1 Year (q_94): -0.70598
• Hazard Rate: -0.42797

COMPARATIVE CONTEXT:
• Global Average at Age 94: -17.1 years
• Regional Rank: Top 23 globally
• Historical Trend: Improving

Based on 262,276 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.


Instruction: What is the occupational mortality rate for Construction workers?

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Construction
Fatal Injury Rate: 13.6 per 100,000 full-time workers
Annual Deaths: 1,193

LEADING CAUSES:
• Falls: 29%
• Struck by object: 19%
• Electrocution: 8%
• Caught-in/between: 20%

Workers' compensation death benefit: $385,894

Human: What is the occupational mortality rate for Construction workers?

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Construction
Fatal Injury Rate: 13.6 per 100,000 full-time workers
Annual Deaths: 1,193

LEADING CAUSES:
• Falls: 29%
• Struck by object: 19%
• Electrocution: 8%
• Caught-in/between: 20%

Workers' compensation death benefit: $385,894


Instruction: What is the mortality rate for Parkinson's in Australia in 2020?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Parkinson's
Location: Australia
Year: 2020
Age Group: All ages

MORTALITY STATISTICS:
• Crude Death Rate: 7.3 per 100,000 population
• Age-Adjusted Rate: 6.6 per 100,000
• Total Deaths: 182,964
• Percentage of All Deaths: 22.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 8.7 per 100,000
• Female Death Rate: 6.2 per 100,000
• Sex Ratio (M:F): 1.23:1

TREND ANALYSIS:
• 5-Year Change: +6.8%
• 10-Year Change: +15.0%
• Annual Percentage Change: -0.6%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #7
• Years of Potential Life Lost (YPLL): 2413229
• Economic Burden: $43.8 billion annually
• Preventable Deaths: 59%

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

International Classification of Diseases (ICD-10): G20
Data Quality: Complete (97% coverage)

Human: What is the mortality rate for Parkinson's in Australia in 2020?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Parkinson's
Location: Australia
Year: 2020
Age Group: All ages

MORTALITY STATISTICS:
• Crude Death Rate: 7.3 per 100,000 population
• Age-Adjusted Rate: 6.6 per 100,000
• Total Deaths: 182,964
• Percentage of All Deaths: 22.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 8.7 per 100,000
• Female Death Rate: 6.2 per 100,000
• Sex Ratio (M:F): 1.23:1

TREND ANALYSIS:
• 5-Year Change: +6.8%
• 10-Year Change: +15.0%
• Annual Percentage Change: -0.6%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #7
• Years of Potential Life Lost (YPLL): 2413229
• Economic Burden: $43.8 billion annually
• Preventable Deaths: 59%

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

International Classification of Diseases (ICD-10): G20
Data Quality: Complete (97% coverage)


Instruction: Calculate the present value of a life annuity for a 49 year old at 2.4% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 49
• Interest Rate (i): 2.36%
• Discount Factor (v): 0.976965
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_49): 19.9245
• Whole Life Annuity-Immediate (a_49): 18.9245
• Temporary Annuity-Due (ä_49:20⌉): 17.6422
• Deferred Annuity (₁₀|ä_49): 13.1425

COMMUTATION FUNCTIONS:
• D_49 = v^49 × l_49: 2932.62
• N_49 = Σ D_k (k≥49): 24690.75
• S_49 = Σ N_k (k≥49): 332411.90

CALCULATION:
ä_49 = N_49 / D_49 = 19.9245

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.870

Present Value of $1,000/month for life: $19709207.36

Human: Calculate the present value of a life annuity for a 49 year old at 2.4% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 49
• Interest Rate (i): 2.36%
• Discount Factor (v): 0.976965
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_49): 19.9245
• Whole Life Annuity-Immediate (a_49): 18.9245
• Temporary Annuity-Due (ä_49:20⌉): 17.6422
• Deferred Annuity (₁₀|ä_49): 13.1425

COMMUTATION FUNCTIONS:
• D_49 = v^49 × l_49: 2932.62
• N_49 = Σ D_k (k≥49): 24690.75
• S_49 = Σ N_k (k≥49): 332411.90

CALCULATION:
ä_49 = N_49 / D_49 = 19.9245

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.870

Present Value of $1,000/month for life: $19709207.36


Instruction: Calculate Whole Life life insurance premium for 60 year old male, $750,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 60
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.003272
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 52% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5153.46
• Expense Charge: $1288.37
• Reserve Accumulation: $1717.82
• Profit Margin: $429.46
• Gross Annual Premium: $8589.10

PAYMENT OPTIONS:
• Annual: $8589.10
• Semi-Annual: $4466.33 (x2 = $8932.67/year)
• Quarterly: $2276.11 (x4 = $9104.45/year)
• Monthly: $773.02 (x12 = $9276.23/year)

RESERVE CALCULATIONS:
• Net Level Premium: $6441.83
• First Year Reserve: $1717.82
• Terminal Reserve (Year 5): $276328.73

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.4%
Profit Margin: 12.4%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 60 year old male, $750,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 60
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.003272
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 52% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5153.46
• Expense Charge: $1288.37
• Reserve Accumulation: $1717.82
• Profit Margin: $429.46
• Gross Annual Premium: $8589.10

PAYMENT OPTIONS:
• Annual: $8589.10
• Semi-Annual: $4466.33 (x2 = $8932.67/year)
• Quarterly: $2276.11 (x4 = $9104.45/year)
• Monthly: $773.02 (x12 = $9276.23/year)

RESERVE CALCULATIONS:
• Net Level Premium: $6441.83
• First Year Reserve: $1717.82
• Terminal Reserve (Year 5): $276328.73

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.4%
Profit Margin: 12.4%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.