Instruction: Compare cardiovascular mortality between Australia, Germany, Russia, Canada and Brazil

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Australia, Germany, Russia, Canada, Brazil
Reference Year: 2022

COMPARATIVE STATISTICS:
• Australia: 192.7 per 100,000 population
• Germany: 127.3 per 100,000 population
• Russia: 214.4 per 100,000 population
• Canada: 135.3 per 100,000 population
• Brazil: 200.4 per 100,000 population

RANKINGS:
1. Germany: 127.3
2. Canada: 135.3
3. Australia: 192.7
4. Brazil: 200.4
5. Russia: 214.4

STATISTICAL ANALYSIS:
• Range: 87.1
• Mean: 174.0
• Median: 192.7
• Standard Deviation: 35.7
• Coefficient of Variation: 20.5%

RELATIVE COMPARISONS:
• Best vs Worst: 1.68x difference
• Above Average: 3/5
• Global Ranking: Australia: #16, Germany: #152, Russia: #65

CONTRIBUTING FACTORS:
• Healthcare System: 34% of variation
• Economic Development: 24% of variation
• Public Health Policy: 10% of variation
• Demographics: 10% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.6% annually

Human: Compare cardiovascular mortality between Australia, Germany, Russia, Canada and Brazil

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Australia, Germany, Russia, Canada, Brazil
Reference Year: 2022

COMPARATIVE STATISTICS:
• Australia: 192.7 per 100,000 population
• Germany: 127.3 per 100,000 population
• Russia: 214.4 per 100,000 population
• Canada: 135.3 per 100,000 population
• Brazil: 200.4 per 100,000 population

RANKINGS:
1. Germany: 127.3
2. Canada: 135.3
3. Australia: 192.7
4. Brazil: 200.4
5. Russia: 214.4

STATISTICAL ANALYSIS:
• Range: 87.1
• Mean: 174.0
• Median: 192.7
• Standard Deviation: 35.7
• Coefficient of Variation: 20.5%

RELATIVE COMPARISONS:
• Best vs Worst: 1.68x difference
• Above Average: 3/5
• Global Ranking: Australia: #16, Germany: #152, Russia: #65

CONTRIBUTING FACTORS:
• Healthcare System: 34% of variation
• Economic Development: 24% of variation
• Public Health Policy: 10% of variation
• Demographics: 10% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.6% annually


Instruction: Show survival curve for India male in 2024

Response:
SURVIVAL CURVE ANALYSIS

Population: India Male
Reference Year: 2024
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         81.1
    1          99,997           15         0.00015         75.5
    5          99,982           28         0.00028         75.1
   10          99,954           85         0.00085         74.9
   20          99,869          164         0.00164         57.6
   30          99,705          276         0.00277         52.8
   40          99,429          334         0.00336         39.0
   50          99,095          671         0.00677         30.4
   60          98,424          931         0.00946         17.7
   70          97,493        1,276         0.01309         14.5
   80          96,217        2,329         0.02421          0.6
   90          93,888        2,271         0.02419          2.2
  100          91,617        4,001         0.04367          4.0
  110          87,616       87,616         1.00000          1.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.2%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.83

The survival curve follows Gompertz law after age 30.
Data sourced from 433,481 death certificates.

Human: Show survival curve for India male in 2024

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: India Male
Reference Year: 2024
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         81.1
    1          99,997           15         0.00015         75.5
    5          99,982           28         0.00028         75.1
   10          99,954           85         0.00085         74.9
   20          99,869          164         0.00164         57.6
   30          99,705          276         0.00277         52.8
   40          99,429          334         0.00336         39.0
   50          99,095          671         0.00677         30.4
   60          98,424          931         0.00946         17.7
   70          97,493        1,276         0.01309         14.5
   80          96,217        2,329         0.02421          0.6
   90          93,888        2,271         0.02419          2.2
  100          91,617        4,001         0.04367          4.0
  110          87,616       87,616         1.00000          1.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.2%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.83

The survival curve follows Gompertz law after age 30.
Data sourced from 433,481 death certificates.


Instruction: Calculate policy reserve for 38 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: 28
• Current Age: 38
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $601.58
• Present Value Future Benefits (PVFB): $43565.00
• Present Value Future Premiums (PVFP): $35357.22

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $10589.37
• Per $1,000 Face: $105.89

PROSPECTIVE METHOD:
• A₁_38:10⌉ = 0.1854
• ä_38:10⌉ = 9.4741
• ₁₀V = 100,000 × A₁ - P × ä = $10589.37

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8582.86
• Accumulated Cost of Insurance: $4792.08
• Interest Earned: $1836.32
• ₁₀V = $10589.37

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $10059.90
• Tax Reserve: $9742.22
• GAAP Reserve: $11118.84

Human: Calculate policy reserve for 38 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: 28
• Current Age: 38
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $601.58
• Present Value Future Benefits (PVFB): $43565.00
• Present Value Future Premiums (PVFP): $35357.22

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $10589.37
• Per $1,000 Face: $105.89

PROSPECTIVE METHOD:
• A₁_38:10⌉ = 0.1854
• ä_38:10⌉ = 9.4741
• ₁₀V = 100,000 × A₁ - P × ä = $10589.37

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8582.86
• Accumulated Cost of Insurance: $4792.08
• Interest Earned: $1836.32
• ₁₀V = $10589.37

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $10059.90
• Tax Reserve: $9742.22
• GAAP Reserve: $11118.84


Instruction: Show survival curve for China female in 2019

Response:
SURVIVAL CURVE ANALYSIS

Population: China Female
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         84.3
    1          99,998            8         0.00008         83.2
    5          99,990           21         0.00021         71.2
   10          99,969           63         0.00063         66.5
   20          99,906          129         0.00129         63.7
   30          99,777          201         0.00201         53.9
   40          99,576          310         0.00311         35.2
   50          99,266          472         0.00475         28.2
   60          98,794          581         0.00588         16.1
   70          98,213        1,044         0.01063          6.6
   80          97,169        1,449         0.01491          3.3
   90          95,720        1,735         0.01813          4.7
  100          93,985        2,785         0.02963          1.6
  110          91,200       91,200         1.00000          2.2

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 77.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.2%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.71

The survival curve follows Gompertz law after age 30.
Data sourced from 487,015 death certificates.

Human: Show survival curve for China female in 2019

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: China Female
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         84.3
    1          99,998            8         0.00008         83.2
    5          99,990           21         0.00021         71.2
   10          99,969           63         0.00063         66.5
   20          99,906          129         0.00129         63.7
   30          99,777          201         0.00201         53.9
   40          99,576          310         0.00311         35.2
   50          99,266          472         0.00475         28.2
   60          98,794          581         0.00588         16.1
   70          98,213        1,044         0.01063          6.6
   80          97,169        1,449         0.01491          3.3
   90          95,720        1,735         0.01813          4.7
  100          93,985        2,785         0.02963          1.6
  110          91,200       91,200         1.00000          2.2

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 77.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.2%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.71

The survival curve follows Gompertz law after age 30.
Data sourced from 487,015 death certificates.


Instruction: Calculate Variable Universal Life life insurance premium for 21 year old female, $100,000 coverage, Preferred 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: 21
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_21): 0.000527
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 64% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $79.09
• Expense Charge: $19.77
• Reserve Accumulation: $26.36
• Profit Margin: $6.59
• Gross Annual Premium: $131.82

PAYMENT OPTIONS:
• Annual: $131.82
• Semi-Annual: $68.55 (x2 = $137.09/year)
• Quarterly: $34.93 (x4 = $139.73/year)
• Monthly: $11.86 (x12 = $142.37/year)

RESERVE CALCULATIONS:
• Net Level Premium: $98.87
• First Year Reserve: $26.36
• Terminal Reserve (Year 44): $36308.35

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

Internal Rate of Return: 10.3%
Profit Margin: 10.8%
Lapse Assumption: 6.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 21 year old female, $100,000 coverage, Preferred 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: 21
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_21): 0.000527
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 64% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $79.09
• Expense Charge: $19.77
• Reserve Accumulation: $26.36
• Profit Margin: $6.59
• Gross Annual Premium: $131.82

PAYMENT OPTIONS:
• Annual: $131.82
• Semi-Annual: $68.55 (x2 = $137.09/year)
• Quarterly: $34.93 (x4 = $139.73/year)
• Monthly: $11.86 (x12 = $142.37/year)

RESERVE CALCULATIONS:
• Net Level Premium: $98.87
• First Year Reserve: $26.36
• Terminal Reserve (Year 44): $36308.35

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

Internal Rate of Return: 10.3%
Profit Margin: 10.8%
Lapse Assumption: 6.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Term life insurance premium for 20 year old female, $250,000 coverage, 15 year term, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 20
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000765
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 50% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $114.75
• Expense Charge: $28.69
• Reserve Accumulation: $38.25
• Profit Margin: $9.56
• Gross Annual Premium: $191.25

PAYMENT OPTIONS:
• Annual: $191.25
• Semi-Annual: $99.45 (x2 = $198.90/year)
• Quarterly: $50.68 (x4 = $202.73/year)
• Monthly: $17.21 (x12 = $206.55/year)

RESERVE CALCULATIONS:
• Net Level Premium: $143.44
• First Year Reserve: $38.25
• Terminal Reserve (Year 15): $103863.48

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

Internal Rate of Return: 9.5%
Profit Margin: 9.7%
Lapse Assumption: 6.7% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 20 year old female, $250,000 coverage, 15 year term, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 20
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000765
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 50% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $114.75
• Expense Charge: $28.69
• Reserve Accumulation: $38.25
• Profit Margin: $9.56
• Gross Annual Premium: $191.25

PAYMENT OPTIONS:
• Annual: $191.25
• Semi-Annual: $99.45 (x2 = $198.90/year)
• Quarterly: $50.68 (x4 = $202.73/year)
• Monthly: $17.21 (x12 = $206.55/year)

RESERVE CALCULATIONS:
• Net Level Premium: $143.44
• First Year Reserve: $38.25
• Terminal Reserve (Year 15): $103863.48

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

Internal Rate of Return: 9.5%
Profit Margin: 9.7%
Lapse Assumption: 6.7% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality trends in Germany from 2010-2022

Response:
MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2010-2022

OVERALL TRENDS:
• Average Annual Change: -1.2%
• Total Change: -13.1%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 2.1 years.
Age-standardized death rate changed by +87 per 100,000.

KEY DRIVERS:
• Medical advances: 37% of improvement
• Public health measures: 17%
• Lifestyle changes: +10%
• Environmental factors: +6%

Human: Analyze mortality trends in Germany from 2010-2022

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2010-2022

OVERALL TRENDS:
• Average Annual Change: -1.2%
• Total Change: -13.1%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 2.1 years.
Age-standardized death rate changed by +87 per 100,000.

KEY DRIVERS:
• Medical advances: 37% of improvement
• Public health measures: 17%
• Lifestyle changes: +10%
• Environmental factors: +6%


Instruction: What is the probability of death within 20 years for someone age 98?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 98 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_98): 0.002371 (0.2371%)
• 20-Year Death Probability (₍20₎q_98): 0.046376 (4.638%)
• Survival Probability (₍20₎p_98): 0.953624 (95.362%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_98): 0.002374
• Hazard Rate (h_98): 0.002374
• Cumulative Hazard (H_98): 0.047486
• Median Future Lifetime: 291.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.4x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 137%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.039420
• Upper Bound: 0.053333

Analysis based on 109,854 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 20 years for someone age 98?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 98 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_98): 0.002371 (0.2371%)
• 20-Year Death Probability (₍20₎q_98): 0.046376 (4.638%)
• Survival Probability (₍20₎p_98): 0.953624 (95.362%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_98): 0.002374
• Hazard Rate (h_98): 0.002374
• Cumulative Hazard (H_98): 0.047486
• Median Future Lifetime: 291.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.4x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 137%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.039420
• Upper Bound: 0.053333

Analysis based on 109,854 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 62 year old male in Germany as of 2021?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Germany
• Age: 62 years
• Sex: Male
• Reference Year: 2021

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 62 (e_62): 14.2 years
• Expected Age at Death: 76.2 years
• Median Survival Time: 9.9 years
• Modal Age at Death: 71.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_62): 72.0%
• 10-Year Survival (₁₀p_62): 51.9%
• 20-Year Survival (₂₀p_62): 26.9%

MORTALITY METRICS:
• Force of Mortality (μ_62): 0.06558
• Probability of Death within 1 Year (q_62): 0.06348
• Hazard Rate: 0.06783

COMPARATIVE CONTEXT:
• Global Average at Age 62: 19.2 years
• Regional Rank: Top 22 globally
• Historical Trend: Improving

Based on 279,931 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.4%.

Human: What is the life expectancy for a 62 year old male in Germany as of 2021?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Germany
• Age: 62 years
• Sex: Male
• Reference Year: 2021

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 62 (e_62): 14.2 years
• Expected Age at Death: 76.2 years
• Median Survival Time: 9.9 years
• Modal Age at Death: 71.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_62): 72.0%
• 10-Year Survival (₁₀p_62): 51.9%
• 20-Year Survival (₂₀p_62): 26.9%

MORTALITY METRICS:
• Force of Mortality (μ_62): 0.06558
• Probability of Death within 1 Year (q_62): 0.06348
• Hazard Rate: 0.06783

COMPARATIVE CONTEXT:
• Global Average at Age 62: 19.2 years
• Regional Rank: Top 22 globally
• Historical Trend: Improving

Based on 279,931 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.4%.


Instruction: Calculate mortality improvement factors for age 54

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 54
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.61%
• Current (2024): 1.40%
• Ultimate (2044+): 0.98%

PROJECTION FACTORS:
• 10-Year Factor: 0.8685
• 20-Year Factor: 0.7542
• 30-Year Factor: 0.6550

Cohort effect adjustment: Applied
Gender-specific: Yes

Human: Calculate mortality improvement factors for age 54

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 54
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.61%
• Current (2024): 1.40%
• Ultimate (2044+): 0.98%

PROJECTION FACTORS:
• 10-Year Factor: 0.8685
• 20-Year Factor: 0.7542
• 30-Year Factor: 0.6550

Cohort effect adjustment: Applied
Gender-specific: Yes


Instruction: Calculate the 5-year death probability for a 65 year old with diabetes

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 65 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_65): 0.001233 (0.1233%)
• 5-Year Death Probability (₍5₎q_65): 0.006150 (0.615%)
• Survival Probability (₍5₎p_65): 0.993850 (99.385%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_65): 0.001234
• Hazard Rate (h_65): 0.001234
• Cumulative Hazard (H_65): 0.006169
• Median Future Lifetime: 561.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.2x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 23%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.005227
• Upper Bound: 0.007072

Analysis based on 194,228 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 5-year death probability for a 65 year old with diabetes

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 65 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_65): 0.001233 (0.1233%)
• 5-Year Death Probability (₍5₎q_65): 0.006150 (0.615%)
• Survival Probability (₍5₎p_65): 0.993850 (99.385%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_65): 0.001234
• Hazard Rate (h_65): 0.001234
• Cumulative Hazard (H_65): 0.006169
• Median Future Lifetime: 561.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.2x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 23%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.005227
• Upper Bound: 0.007072

Analysis based on 194,228 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the mortality rate for Influenza/Pneumonia in Germany for 45-64 in 2023?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: Germany
Year: 2023
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 14.2 per 100,000 population
• Age-Adjusted Rate: 12.6 per 100,000
• Total Deaths: 226,362
• Percentage of All Deaths: 18.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 17.1 per 100,000
• Female Death Rate: 12.1 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: +5.4%
• 10-Year Change: +12.9%
• Annual Percentage Change: +1.5%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 4860122
• Economic Burden: $94.7 billion annually
• Preventable Deaths: 53%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Partial (89% coverage)

Human: What is the mortality rate for Influenza/Pneumonia in Germany for 45-64 in 2023?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: Germany
Year: 2023
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 14.2 per 100,000 population
• Age-Adjusted Rate: 12.6 per 100,000
• Total Deaths: 226,362
• Percentage of All Deaths: 18.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 17.1 per 100,000
• Female Death Rate: 12.1 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: +5.4%
• 10-Year Change: +12.9%
• Annual Percentage Change: +1.5%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 4860122
• Economic Burden: $94.7 billion annually
• Preventable Deaths: 53%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Partial (89% coverage)


Instruction: Calculate policy reserve for 62 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: 52
• Current Age: 62
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $749.84
• Present Value Future Benefits (PVFB): $50092.90
• Present Value Future Premiums (PVFP): $36390.42

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $20568.64
• Per $1,000 Face: $205.69

PROSPECTIVE METHOD:
• A₁_62:10⌉ = 0.2400
• ä_62:10⌉ = 8.3497
• ₁₀V = 100,000 × A₁ - P × ä = $20568.64

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10261.63
• Accumulated Cost of Insurance: $4187.42
• Interest Earned: $1640.06
• ₁₀V = $20568.64

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $19540.20
• Tax Reserve: $18923.15
• GAAP Reserve: $21597.07

Human: Calculate policy reserve for 62 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: 52
• Current Age: 62
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $749.84
• Present Value Future Benefits (PVFB): $50092.90
• Present Value Future Premiums (PVFP): $36390.42

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $20568.64
• Per $1,000 Face: $205.69

PROSPECTIVE METHOD:
• A₁_62:10⌉ = 0.2400
• ä_62:10⌉ = 8.3497
• ₁₀V = 100,000 × A₁ - P × ä = $20568.64

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10261.63
• Accumulated Cost of Insurance: $4187.42
• Interest Earned: $1640.06
• ₁₀V = $20568.64

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $19540.20
• Tax Reserve: $18923.15
• GAAP Reserve: $21597.07


Instruction: What is the mortality rate for Influenza/Pneumonia in France for 65-74 in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: France
Year: 2022
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 15.7 per 100,000 population
• Age-Adjusted Rate: 13.6 per 100,000
• Total Deaths: 87,596
• Percentage of All Deaths: 3.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 18.9 per 100,000
• Female Death Rate: 13.4 per 100,000
• Sex Ratio (M:F): 1.25:1

TREND ANALYSIS:
• 5-Year Change: -3.0%
• 10-Year Change: -14.8%
• Annual Percentage Change: +1.6%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 1227933
• Economic Burden: $57.0 billion annually
• Preventable Deaths: 28%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Near-Complete (85% coverage)

Human: What is the mortality rate for Influenza/Pneumonia in France for 65-74 in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: France
Year: 2022
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 15.7 per 100,000 population
• Age-Adjusted Rate: 13.6 per 100,000
• Total Deaths: 87,596
• Percentage of All Deaths: 3.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 18.9 per 100,000
• Female Death Rate: 13.4 per 100,000
• Sex Ratio (M:F): 1.25:1

TREND ANALYSIS:
• 5-Year Change: -3.0%
• 10-Year Change: -14.8%
• Annual Percentage Change: +1.6%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 1227933
• Economic Burden: $57.0 billion annually
• Preventable Deaths: 28%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Near-Complete (85% coverage)


Instruction: Analyze mortality differences by education in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Education
Country: USA
Analysis Period: 2022

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 701.7
• High School: 1021.0
• Some College: 718.2
• Bachelor's: 301.7
• Graduate Degree: 1061.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.90
• Rate Difference: 286.3 per 100,000
• Population Attributable Risk: 21.5%
• Gini Coefficient: 0.280

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 83.0 years
• High School: 77.5 years
• Some College: 70.9 years
• Bachelor's: 81.7 years
• Graduate Degree: 74.5 years

CONTRIBUTING FACTORS:
• Healthcare Access: 23% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 14% of disparity
• Biological Factors: 11% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -0.9%

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: 2022

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 701.7
• High School: 1021.0
• Some College: 718.2
• Bachelor's: 301.7
• Graduate Degree: 1061.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.90
• Rate Difference: 286.3 per 100,000
• Population Attributable Risk: 21.5%
• Gini Coefficient: 0.280

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 83.0 years
• High School: 77.5 years
• Some College: 70.9 years
• Bachelor's: 81.7 years
• Graduate Degree: 74.5 years

CONTRIBUTING FACTORS:
• Healthcare Access: 23% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 14% of disparity
• Biological Factors: 11% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -0.9%

Social determinants explain 61% of observed mortality differences.


Instruction: Calculate Variable Universal Life life insurance premium for 20 year old female, $2,000,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 20
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000510
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 53% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1530.00
• Expense Charge: $382.50
• Reserve Accumulation: $510.00
• Profit Margin: $127.50
• Gross Annual Premium: $2550.00

PAYMENT OPTIONS:
• Annual: $2550.00
• Semi-Annual: $1326.00 (x2 = $2652.00/year)
• Quarterly: $675.75 (x4 = $2703.00/year)
• Monthly: $229.50 (x12 = $2754.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1912.50
• First Year Reserve: $510.00
• Terminal Reserve (Year 45): $1399516.24

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 25 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 10.3%
Profit Margin: 12.7%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 20 year old female, $2,000,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 20
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000510
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 53% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1530.00
• Expense Charge: $382.50
• Reserve Accumulation: $510.00
• Profit Margin: $127.50
• Gross Annual Premium: $2550.00

PAYMENT OPTIONS:
• Annual: $2550.00
• Semi-Annual: $1326.00 (x2 = $2652.00/year)
• Quarterly: $675.75 (x4 = $2703.00/year)
• Monthly: $229.50 (x12 = $2754.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1912.50
• First Year Reserve: $510.00
• Terminal Reserve (Year 45): $1399516.24

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 25 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 10.3%
Profit Margin: 12.7%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare maternal mortality between Australia, Spain and Mexico

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Australia, Spain, Mexico
Reference Year: 2023

COMPARATIVE STATISTICS:
• Australia: 17.2 per 100,000 live births
• Spain: 15.5 per 100,000 live births
• Mexico: 4.9 per 100,000 live births

RANKINGS:
1. Mexico: 4.9
2. Spain: 15.5
3. Australia: 17.2

STATISTICAL ANALYSIS:
• Range: 12.2
• Mean: 12.5
• Median: 15.5
• Standard Deviation: 5.4
• Coefficient of Variation: 43.3%

RELATIVE COMPARISONS:
• Best vs Worst: 3.48x difference
• Above Average: 2/3
• Global Ranking: Australia: #101, Spain: #54, Mexico: #142

CONTRIBUTING FACTORS:
• Healthcare System: 33% of variation
• Economic Development: 28% of variation
• Public Health Policy: 25% of variation
• Demographics: 14% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.9% annually

Human: Compare maternal mortality between Australia, Spain and Mexico

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Australia, Spain, Mexico
Reference Year: 2023

COMPARATIVE STATISTICS:
• Australia: 17.2 per 100,000 live births
• Spain: 15.5 per 100,000 live births
• Mexico: 4.9 per 100,000 live births

RANKINGS:
1. Mexico: 4.9
2. Spain: 15.5
3. Australia: 17.2

STATISTICAL ANALYSIS:
• Range: 12.2
• Mean: 12.5
• Median: 15.5
• Standard Deviation: 5.4
• Coefficient of Variation: 43.3%

RELATIVE COMPARISONS:
• Best vs Worst: 3.48x difference
• Above Average: 2/3
• Global Ranking: Australia: #101, Spain: #54, Mexico: #142

CONTRIBUTING FACTORS:
• Healthcare System: 33% of variation
• Economic Development: 28% of variation
• Public Health Policy: 25% of variation
• Demographics: 14% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.9% annually


Instruction: Calculate policy reserve for 46 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: 36
• Current Age: 46
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1416.25
• Present Value Future Benefits (PVFB): $44285.44
• Present Value Future Premiums (PVFP): $39301.39

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $29252.70
• Per $1,000 Face: $292.53

PROSPECTIVE METHOD:
• A₁_46:10⌉ = 0.1549
• ä_46:10⌉ = 8.3513
• ₁₀V = 100,000 × A₁ - P × ä = $29252.70

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11991.52
• Accumulated Cost of Insurance: $4084.50
• Interest Earned: $1656.67
• ₁₀V = $29252.70

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $27790.07
• Tax Reserve: $26912.49
• GAAP Reserve: $30715.34

Human: Calculate policy reserve for 46 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: 36
• Current Age: 46
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1416.25
• Present Value Future Benefits (PVFB): $44285.44
• Present Value Future Premiums (PVFP): $39301.39

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $29252.70
• Per $1,000 Face: $292.53

PROSPECTIVE METHOD:
• A₁_46:10⌉ = 0.1549
• ä_46:10⌉ = 8.3513
• ₁₀V = 100,000 × A₁ - P × ä = $29252.70

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11991.52
• Accumulated Cost of Insurance: $4084.50
• Interest Earned: $1656.67
• ₁₀V = $29252.70

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $27790.07
• Tax Reserve: $26912.49
• GAAP Reserve: $30715.34


Instruction: Calculate Whole Life life insurance premium for 70 year old male, $500,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 70
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_70): 0.006089
• Underwriting Multiplier: 1.0x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 84% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6393.10
• Expense Charge: $1598.27
• Reserve Accumulation: $2131.03
• Profit Margin: $532.76
• Gross Annual Premium: $10655.16

PAYMENT OPTIONS:
• Annual: $10655.16
• Semi-Annual: $5540.68 (x2 = $11081.37/year)
• Quarterly: $2823.62 (x4 = $11294.47/year)
• Monthly: $958.96 (x12 = $11507.57/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7991.37
• First Year Reserve: $2131.03
• Terminal Reserve (Year -5): $285035.81

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

Internal Rate of Return: 8.0%
Profit Margin: 11.7%
Lapse Assumption: 5.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 70 year old male, $500,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 70
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_70): 0.006089
• Underwriting Multiplier: 1.0x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 84% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6393.10
• Expense Charge: $1598.27
• Reserve Accumulation: $2131.03
• Profit Margin: $532.76
• Gross Annual Premium: $10655.16

PAYMENT OPTIONS:
• Annual: $10655.16
• Semi-Annual: $5540.68 (x2 = $11081.37/year)
• Quarterly: $2823.62 (x4 = $11294.47/year)
• Monthly: $958.96 (x12 = $11507.57/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7991.37
• First Year Reserve: $2131.03
• Terminal Reserve (Year -5): $285035.81

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

Internal Rate of Return: 8.0%
Profit Margin: 11.7%
Lapse Assumption: 5.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate the 20-year death probability for a 10 year oldsmoker with obesity

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 10 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_10): 0.000519 (0.0519%)
• 20-Year Death Probability (₍20₎q_10): 0.010335 (1.033%)
• Survival Probability (₍20₎p_10): 0.989665 (98.967%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_10): 0.000519
• Hazard Rate (h_10): 0.000519
• Cumulative Hazard (H_10): 0.010388
• Median Future Lifetime: 1334.5 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.008785
• Upper Bound: 0.011885

Analysis based on 70,082 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 20-year death probability for a 10 year oldsmoker with obesity

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 10 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_10): 0.000519 (0.0519%)
• 20-Year Death Probability (₍20₎q_10): 0.010335 (1.033%)
• Survival Probability (₍20₎p_10): 0.989665 (98.967%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_10): 0.000519
• Hazard Rate (h_10): 0.000519
• Cumulative Hazard (H_10): 0.010388
• Median Future Lifetime: 1334.5 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.008785
• Upper Bound: 0.011885

Analysis based on 70,082 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 58 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: 48
• Current Age: 58
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1488.53
• Present Value Future Benefits (PVFB): $52355.54
• Present Value Future Premiums (PVFP): $30996.78

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $36298.98
• Per $1,000 Face: $362.99

PROSPECTIVE METHOD:
• A₁_58:10⌉ = 0.1572
• ä_58:10⌉ = 9.2598
• ₁₀V = 100,000 × A₁ - P × ä = $36298.98

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9692.03
• Accumulated Cost of Insurance: $4224.41
• Interest Earned: $1130.73
• ₁₀V = $36298.98

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $34484.03
• Tax Reserve: $33395.06
• GAAP Reserve: $38113.92

Human: Calculate policy reserve for 58 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: 48
• Current Age: 58
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1488.53
• Present Value Future Benefits (PVFB): $52355.54
• Present Value Future Premiums (PVFP): $30996.78

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $36298.98
• Per $1,000 Face: $362.99

PROSPECTIVE METHOD:
• A₁_58:10⌉ = 0.1572
• ä_58:10⌉ = 9.2598
• ₁₀V = 100,000 × A₁ - P × ä = $36298.98

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9692.03
• Accumulated Cost of Insurance: $4224.41
• Interest Earned: $1130.73
• ₁₀V = $36298.98

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $34484.03
• Tax Reserve: $33395.06
• GAAP Reserve: $38113.92


Instruction: Analyze mortality impact of H1N1

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 439,560
Case Fatality Rate: 3.8%
Infection Fatality Rate: 0.44%

Age-specific mortality shows exponential increase with age.
Economic impact: $9.5 trillion globally.

Human: Analyze mortality impact of H1N1

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 439,560
Case Fatality Rate: 3.8%
Infection Fatality Rate: 0.44%

Age-specific mortality shows exponential increase with age.
Economic impact: $9.5 trillion globally.


Instruction: Calculate Term life insurance premium for 46 year old male, $250,000 coverage, 30 year term, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 30 years
• Issue Age: 46
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_46): 0.002052
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 57% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $307.78
• Expense Charge: $76.94
• Reserve Accumulation: $102.59
• Profit Margin: $25.65
• Gross Annual Premium: $512.96

PAYMENT OPTIONS:
• Annual: $512.96
• Semi-Annual: $266.74 (x2 = $533.48/year)
• Quarterly: $135.94 (x4 = $543.74/year)
• Monthly: $46.17 (x12 = $554.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $384.72
• First Year Reserve: $102.59
• Terminal Reserve (Year 30): $169956.75

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

Internal Rate of Return: 9.8%
Profit Margin: 12.1%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 46 year old male, $250,000 coverage, 30 year term, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 30 years
• Issue Age: 46
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_46): 0.002052
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 57% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $307.78
• Expense Charge: $76.94
• Reserve Accumulation: $102.59
• Profit Margin: $25.65
• Gross Annual Premium: $512.96

PAYMENT OPTIONS:
• Annual: $512.96
• Semi-Annual: $266.74 (x2 = $533.48/year)
• Quarterly: $135.94 (x4 = $543.74/year)
• Monthly: $46.17 (x12 = $554.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $384.72
• First Year Reserve: $102.59
• Terminal Reserve (Year 30): $169956.75

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

Internal Rate of Return: 9.8%
Profit Margin: 12.1%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare suburban vs other area mortality rates in UK

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 836.1
• Rural: 922.7
• Suburban: 752.6

Rural areas show 10.4% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare suburban vs other area mortality rates in UK

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 836.1
• Rural: 922.7
• Suburban: 752.6

Rural areas show 10.4% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2022

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 1134.1
• $25-50k: 1173.8
• $50-75k: 752.6
• $75-100k: 563.7
• >$100k: 1090.6

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.84
• Rate Difference: 247.5 per 100,000
• Population Attributable Risk: 36.6%
• Gini Coefficient: 0.129

LIFE EXPECTANCY BY INCOME:
• <$25k: 72.8 years
• $25-50k: 82.2 years
• $50-75k: 71.8 years
• $75-100k: 83.6 years
• >$100k: 73.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 25% of disparity
• Socioeconomic Status: 18% of disparity
• Environmental Factors: 21% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 11% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.8%

Social determinants explain 70% 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: 2022

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 1134.1
• $25-50k: 1173.8
• $50-75k: 752.6
• $75-100k: 563.7
• >$100k: 1090.6

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.84
• Rate Difference: 247.5 per 100,000
• Population Attributable Risk: 36.6%
• Gini Coefficient: 0.129

LIFE EXPECTANCY BY INCOME:
• <$25k: 72.8 years
• $25-50k: 82.2 years
• $50-75k: 71.8 years
• $75-100k: 83.6 years
• >$100k: 73.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 25% of disparity
• Socioeconomic Status: 18% of disparity
• Environmental Factors: 21% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 11% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.8%

Social determinants explain 70% of observed mortality differences.


Instruction: Calculate excess mortality during 2021 cold snap in Italy for 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: Italy
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 37,175
• Observed Deaths: 47,670
• Excess Deaths: 10,495
• Excess Mortality Rate: 28.2%
• P-score: 28.2%
• Z-score: 3.25 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -4.3% (1,049 deaths)
• 45-64 years: 18.0% (2,623 deaths)
• 65-74 years: 27.2% (2,623 deaths)
• 75+ years: 36.2% (4,198 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 7,955 (64%)
• Indirect (probable): 1,636 (15%)
• Collateral (delayed care): 1,556 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,920, 12,069]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 130150
Economic Impact: $9.8 billion
Quality-Adjusted Life Years Lost: 106285

Human: Calculate excess mortality during 2021 cold snap in Italy for 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: Italy
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 37,175
• Observed Deaths: 47,670
• Excess Deaths: 10,495
• Excess Mortality Rate: 28.2%
• P-score: 28.2%
• Z-score: 3.25 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -4.3% (1,049 deaths)
• 45-64 years: 18.0% (2,623 deaths)
• 65-74 years: 27.2% (2,623 deaths)
• 75+ years: 36.2% (4,198 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 7,955 (64%)
• Indirect (probable): 1,636 (15%)
• Collateral (delayed care): 1,556 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,920, 12,069]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 130150
Economic Impact: $9.8 billion
Quality-Adjusted Life Years Lost: 106285


Instruction: What is the life expectancy for a 90 year old female in Japan as of 2024?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 90 years
• Sex: Female
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 90 (e_90): 3.2 years
• Expected Age at Death: 93.2 years
• Median Survival Time: 2.2 years
• Modal Age at Death: 88.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_90): 30.4%
• 10-Year Survival (₁₀p_90): 9.2%
• 20-Year Survival (₂₀p_90): 0.9%

MORTALITY METRICS:
• Force of Mortality (μ_90): 0.23807
• Probability of Death within 1 Year (q_90): 0.21185
• Hazard Rate: 0.27190

COMPARATIVE CONTEXT:
• Global Average at Age 90: -5.4 years
• Regional Rank: Top 32 globally
• Historical Trend: Stable

Based on 214,490 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.7%.

Human: What is the life expectancy for a 90 year old female in Japan as of 2024?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 90 years
• Sex: Female
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 90 (e_90): 3.2 years
• Expected Age at Death: 93.2 years
• Median Survival Time: 2.2 years
• Modal Age at Death: 88.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_90): 30.4%
• 10-Year Survival (₁₀p_90): 9.2%
• 20-Year Survival (₂₀p_90): 0.9%

MORTALITY METRICS:
• Force of Mortality (μ_90): 0.23807
• Probability of Death within 1 Year (q_90): 0.21185
• Hazard Rate: 0.27190

COMPARATIVE CONTEXT:
• Global Average at Age 90: -5.4 years
• Regional Rank: Top 32 globally
• Historical Trend: Stable

Based on 214,490 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.7%.


Instruction: Show survival curve for India female in 2020

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         77.1
    1          99,998            9         0.00009         77.8
    5          99,989           20         0.00020         78.2
   10          99,969           53         0.00053         74.6
   20          99,916          120         0.00120         62.7
   30          99,796          201         0.00201         51.1
   40          99,595          317         0.00318         42.0
   50          99,278          410         0.00413         32.8
   60          98,868          597         0.00604         25.0
   70          98,271        1,135         0.01155         12.8
   80          97,136        1,667         0.01716          0.0
   90          95,469        2,268         0.02376          3.6
  100          93,201        2,977         0.03194          2.0
  110          90,224       90,224         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.1%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.77

The survival curve follows Gompertz law after age 30.
Data sourced from 233,041 death certificates.

Human: Show survival curve for India female in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         77.1
    1          99,998            9         0.00009         77.8
    5          99,989           20         0.00020         78.2
   10          99,969           53         0.00053         74.6
   20          99,916          120         0.00120         62.7
   30          99,796          201         0.00201         51.1
   40          99,595          317         0.00318         42.0
   50          99,278          410         0.00413         32.8
   60          98,868          597         0.00604         25.0
   70          98,271        1,135         0.01155         12.8
   80          97,136        1,667         0.01716          0.0
   90          95,469        2,268         0.02376          3.6
  100          93,201        2,977         0.03194          2.0
  110          90,224       90,224         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 79.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.1%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.77

The survival curve follows Gompertz law after age 30.
Data sourced from 233,041 death certificates.


Instruction: Calculate the present value of a life annuity for a 62 year old at 2.3% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 62
• Interest Rate (i): 2.25%
• Discount Factor (v): 0.977985
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_62): 11.9273
• Whole Life Annuity-Immediate (a_62): 10.9273
• Temporary Annuity-Due (ä_62:20⌉): 11.9273
• Deferred Annuity (₁₀|ä_62): 6.9383

COMMUTATION FUNCTIONS:
• D_62 = v^62 × l_62: 2856.64
• N_62 = Σ D_k (k≥62): 39630.91
• S_62 = Σ N_k (k≥62): 372283.08

CALCULATION:
ä_62 = N_62 / D_62 = 11.9273

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.876

Present Value of $1,000/month for life: $11804257.70

Human: Calculate the present value of a life annuity for a 62 year old at 2.3% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 62
• Interest Rate (i): 2.25%
• Discount Factor (v): 0.977985
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_62): 11.9273
• Whole Life Annuity-Immediate (a_62): 10.9273
• Temporary Annuity-Due (ä_62:20⌉): 11.9273
• Deferred Annuity (₁₀|ä_62): 6.9383

COMMUTATION FUNCTIONS:
• D_62 = v^62 × l_62: 2856.64
• N_62 = Σ D_k (k≥62): 39630.91
• S_62 = Σ N_k (k≥62): 372283.08

CALCULATION:
ä_62 = N_62 / D_62 = 11.9273

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.876

Present Value of $1,000/month for life: $11804257.70


Instruction: Compare cancer mortality between Brazil, Japan and Mexico

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Brazil, Japan, Mexico
Reference Year: 2020

COMPARATIVE STATISTICS:
• Brazil: 108.0 per 100,000 population
• Japan: 215.7 per 100,000 population
• Mexico: 205.8 per 100,000 population

RANKINGS:
1. Brazil: 108.0
2. Mexico: 205.8
3. Japan: 215.7

STATISTICAL ANALYSIS:
• Range: 107.6
• Mean: 176.5
• Median: 205.8
• Standard Deviation: 48.6
• Coefficient of Variation: 27.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.00x difference
• Above Average: 2/3
• Global Ranking: Brazil: #8, Japan: #177, Mexico: #147

CONTRIBUTING FACTORS:
• Healthcare System: 37% of variation
• Economic Development: 35% of variation
• Public Health Policy: 10% of variation
• Demographics: 11% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 1.6% annually

Human: Compare cancer mortality between Brazil, Japan and Mexico

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Brazil, Japan, Mexico
Reference Year: 2020

COMPARATIVE STATISTICS:
• Brazil: 108.0 per 100,000 population
• Japan: 215.7 per 100,000 population
• Mexico: 205.8 per 100,000 population

RANKINGS:
1. Brazil: 108.0
2. Mexico: 205.8
3. Japan: 215.7

STATISTICAL ANALYSIS:
• Range: 107.6
• Mean: 176.5
• Median: 205.8
• Standard Deviation: 48.6
• Coefficient of Variation: 27.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.00x difference
• Above Average: 2/3
• Global Ranking: Brazil: #8, Japan: #177, Mexico: #147

CONTRIBUTING FACTORS:
• Healthcare System: 37% of variation
• Economic Development: 35% of variation
• Public Health Policy: 10% of variation
• Demographics: 11% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 1.6% annually


Instruction: Mortality risk assessment for 94 year old over next 1 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 94 years
• Assessment Period: 1 year
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_94): 0.010925 (1.0925%)
• 1-Year Death Probability (₍1₎q_94): 0.010925 (1.093%)
• Survival Probability (₍1₎p_94): 0.989075 (98.907%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_94): 0.010985
• Hazard Rate (h_94): 0.010985
• Cumulative Hazard (H_94): 0.010985
• Median Future Lifetime: 63.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 10.9x standard
• Risk Category: Substandard
• Insurability: Standard with loading
• Recommended Premium Loading: 993%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.009286
• Upper Bound: 0.012564

Analysis based on 147,367 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 94 year old over next 1 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 94 years
• Assessment Period: 1 year
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_94): 0.010925 (1.0925%)
• 1-Year Death Probability (₍1₎q_94): 0.010925 (1.093%)
• Survival Probability (₍1₎p_94): 0.989075 (98.907%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_94): 0.010985
• Hazard Rate (h_94): 0.010985
• Cumulative Hazard (H_94): 0.010985
• Median Future Lifetime: 63.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 10.9x standard
• Risk Category: Substandard
• Insurability: Standard with loading
• Recommended Premium Loading: 993%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.009286
• Upper Bound: 0.012564

Analysis based on 147,367 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Compare urban vs other area mortality rates in UK

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 772.6
• Rural: 862.0
• Suburban: 701.7

Rural areas show 11.6% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare urban vs other area mortality rates in UK

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 772.6
• Rural: 862.0
• Suburban: 701.7

Rural areas show 11.6% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: What are the mortality characteristics for adolescent population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Adolescent (13-19 years)

MORTALITY METRICS:
• Death Rate: 14.22 per 1,000
• Leading Causes: Accidents, suicide, homicide
• Preventable Deaths: 47%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for adolescent population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Adolescent (13-19 years)

MORTALITY METRICS:
• Death Rate: 14.22 per 1,000
• Leading Causes: Accidents, suicide, homicide
• Preventable Deaths: 47%

Life table analysis shows stable risk profile.


Instruction: Analyze mortality differences by ethnicity in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Ethnicity
Country: USA
Analysis Period: 2019

MORTALITY RATES BY ETHNICITY (per 100,000):
• Non-Hispanic White: 669.1
• Hispanic: 820.4
• Non-Hispanic Black: 571.1
• Asian/Pacific Islander: 720.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.38
• Rate Difference: 617.0 per 100,000
• Population Attributable Risk: 21.0%
• Gini Coefficient: 0.328

LIFE EXPECTANCY BY ETHNICITY:
• Non-Hispanic White: 76.7 years
• Hispanic: 76.3 years
• Non-Hispanic Black: 75.9 years
• Asian/Pacific Islander: 80.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 28% of disparity
• Environmental Factors: 23% of disparity
• Behavioral Factors: 16% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.3%

Social determinants explain 65% of observed mortality differences.

Human: Analyze mortality differences by ethnicity in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Ethnicity
Country: USA
Analysis Period: 2019

MORTALITY RATES BY ETHNICITY (per 100,000):
• Non-Hispanic White: 669.1
• Hispanic: 820.4
• Non-Hispanic Black: 571.1
• Asian/Pacific Islander: 720.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.38
• Rate Difference: 617.0 per 100,000
• Population Attributable Risk: 21.0%
• Gini Coefficient: 0.328

LIFE EXPECTANCY BY ETHNICITY:
• Non-Hispanic White: 76.7 years
• Hispanic: 76.3 years
• Non-Hispanic Black: 75.9 years
• Asian/Pacific Islander: 80.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 28% of disparity
• Environmental Factors: 23% of disparity
• Behavioral Factors: 16% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.3%

Social determinants explain 65% of observed mortality differences.


Instruction: Analyze mortality differences by race in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2023

MORTALITY RATES BY RACE (per 100,000):
• White: 889.1
• Black: 795.3
• Asian: 1103.0
• Hispanic: 659.1
• Native American: 651.8

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.03
• Rate Difference: 492.9 per 100,000
• Population Attributable Risk: 21.1%
• Gini Coefficient: 0.128

LIFE EXPECTANCY BY RACE:
• White: 82.7 years
• Black: 75.7 years
• Asian: 77.2 years
• Hispanic: 77.5 years
• Native American: 79.8 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 18% of disparity
• Environmental Factors: 22% of disparity
• Behavioral Factors: 23% of disparity
• Biological Factors: 10% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.9%

Social determinants explain 73% 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: 2023

MORTALITY RATES BY RACE (per 100,000):
• White: 889.1
• Black: 795.3
• Asian: 1103.0
• Hispanic: 659.1
• Native American: 651.8

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.03
• Rate Difference: 492.9 per 100,000
• Population Attributable Risk: 21.1%
• Gini Coefficient: 0.128

LIFE EXPECTANCY BY RACE:
• White: 82.7 years
• Black: 75.7 years
• Asian: 77.2 years
• Hispanic: 77.5 years
• Native American: 79.8 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 18% of disparity
• Environmental Factors: 22% of disparity
• Behavioral Factors: 23% of disparity
• Biological Factors: 10% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.9%

Social determinants explain 73% of observed mortality differences.


Instruction: Calculate mortality improvement factors for age 49

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 49
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.19%
• Current (2024): 2.30%
• Ultimate (2044+): 0.55%

PROJECTION FACTORS:
• 10-Year Factor: 0.7921
• 20-Year Factor: 0.6275
• 30-Year Factor: 0.4970

Cohort effect adjustment: Not applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 49

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 49
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.19%
• Current (2024): 2.30%
• Ultimate (2044+): 0.55%

PROJECTION FACTORS:
• 10-Year Factor: 0.7921
• 20-Year Factor: 0.6275
• 30-Year Factor: 0.4970

Cohort effect adjustment: Not applied
Gender-specific: No


Instruction: Calculate mortality improvement factors for age 65

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 65
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.88%
• Current (2024): 2.24%
• Ultimate (2044+): 0.54%

PROJECTION FACTORS:
• 10-Year Factor: 0.7971
• 20-Year Factor: 0.6353
• 30-Year Factor: 0.5064

Cohort effect adjustment: Applied
Gender-specific: Yes

Human: Calculate mortality improvement factors for age 65

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 65
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.88%
• Current (2024): 2.24%
• Ultimate (2044+): 0.54%

PROJECTION FACTORS:
• 10-Year Factor: 0.7971
• 20-Year Factor: 0.6353
• 30-Year Factor: 0.5064

Cohort effect adjustment: Applied
Gender-specific: Yes


Instruction: Calculate Term life insurance premium for 20 year old female, $1,000,000 coverage, 10 year term, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $1,000,000
• Term Length: 10 years
• Issue Age: 20
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000510
• Underwriting Multiplier: 0.6x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $306.00
• Expense Charge: $76.50
• Reserve Accumulation: $102.00
• Profit Margin: $25.50
• Gross Annual Premium: $510.00

PAYMENT OPTIONS:
• Annual: $510.00
• Semi-Annual: $265.20 (x2 = $530.40/year)
• Quarterly: $135.15 (x4 = $540.60/year)
• Monthly: $45.90 (x12 = $550.80/year)

RESERVE CALCULATIONS:
• Net Level Premium: $382.50
• First Year Reserve: $102.00
• Terminal Reserve (Year 10): $312470.15

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

Internal Rate of Return: 11.6%
Profit Margin: 11.3%
Lapse Assumption: 4.4% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 20 year old female, $1,000,000 coverage, 10 year term, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $1,000,000
• Term Length: 10 years
• Issue Age: 20
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000510
• Underwriting Multiplier: 0.6x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $306.00
• Expense Charge: $76.50
• Reserve Accumulation: $102.00
• Profit Margin: $25.50
• Gross Annual Premium: $510.00

PAYMENT OPTIONS:
• Annual: $510.00
• Semi-Annual: $265.20 (x2 = $530.40/year)
• Quarterly: $135.15 (x4 = $540.60/year)
• Monthly: $45.90 (x12 = $550.80/year)

RESERVE CALCULATIONS:
• Net Level Premium: $382.50
• First Year Reserve: $102.00
• Terminal Reserve (Year 10): $312470.15

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

Internal Rate of Return: 11.6%
Profit Margin: 11.3%
Lapse Assumption: 4.4% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Mortality risk assessment for 79 year old over next 20 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 79 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_79): 0.000956 (0.0956%)
• 20-Year Death Probability (₍20₎q_79): 0.018939 (1.894%)
• Survival Probability (₍20₎p_79): 0.981061 (98.106%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_79): 0.000956
• Hazard Rate (h_79): 0.000956
• Cumulative Hazard (H_79): 0.019121
• Median Future Lifetime: 725.0 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016098
• Upper Bound: 0.021780

Analysis based on 118,796 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 79 year old over next 20 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 79 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_79): 0.000956 (0.0956%)
• 20-Year Death Probability (₍20₎q_79): 0.018939 (1.894%)
• Survival Probability (₍20₎p_79): 0.981061 (98.106%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_79): 0.000956
• Hazard Rate (h_79): 0.000956
• Cumulative Hazard (H_79): 0.019121
• Median Future Lifetime: 725.0 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016098
• Upper Bound: 0.021780

Analysis based on 118,796 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 96 year old both in Italy as of 2022?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 96 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 96 (e_96): 0.0 years
• Expected Age at Death: 96.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 91.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_96): 0.7%
• 10-Year Survival (₁₀p_96): 0.0%
• 20-Year Survival (₂₀p_96): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_96): 1.00000
• Probability of Death within 1 Year (q_96): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 96: -12.6 years
• Regional Rank: Top 44 globally
• Historical Trend: Improving

Based on 497,732 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 5.0%.

Human: What is the life expectancy for a 96 year old both in Italy as of 2022?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 96 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 96 (e_96): 0.0 years
• Expected Age at Death: 96.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 91.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_96): 0.7%
• 10-Year Survival (₁₀p_96): 0.0%
• 20-Year Survival (₂₀p_96): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_96): 1.00000
• Probability of Death within 1 Year (q_96): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 96: -12.6 years
• Regional Rank: Top 44 globally
• Historical Trend: Improving

Based on 497,732 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 5.0%.


Instruction: What is the life expectancy for a 32 year old female in Canada as of 2015?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 32 years
• Sex: Female
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 32 (e_32): 58.6 years
• Expected Age at Death: 90.6 years
• Median Survival Time: 40.6 years
• Modal Age at Death: 85.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_32): 92.0%
• 10-Year Survival (₁₀p_32): 84.6%
• 20-Year Survival (₂₀p_32): 71.5%

MORTALITY METRICS:
• Force of Mortality (μ_32): 0.01678
• Probability of Death within 1 Year (q_32): 0.01664
• Hazard Rate: 0.01692

COMPARATIVE CONTEXT:
• Global Average at Age 32: 50.1 years
• Regional Rank: Top 32 globally
• Historical Trend: Improving

Based on 410,191 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.2%.

Human: What is the life expectancy for a 32 year old female in Canada as of 2015?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 32 years
• Sex: Female
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 32 (e_32): 58.6 years
• Expected Age at Death: 90.6 years
• Median Survival Time: 40.6 years
• Modal Age at Death: 85.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_32): 92.0%
• 10-Year Survival (₁₀p_32): 84.6%
• 20-Year Survival (₂₀p_32): 71.5%

MORTALITY METRICS:
• Force of Mortality (μ_32): 0.01678
• Probability of Death within 1 Year (q_32): 0.01664
• Hazard Rate: 0.01692

COMPARATIVE CONTEXT:
• Global Average at Age 32: 50.1 years
• Regional Rank: Top 32 globally
• Historical Trend: Improving

Based on 410,191 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.2%.


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

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 30 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease, obesity, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_30): 0.002419 (0.2419%)
• 30-Year Death Probability (₍30₎q_30): 0.070077 (7.008%)
• Survival Probability (₍30₎p_30): 0.929923 (92.992%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_30): 0.002422
• Hazard Rate (h_30): 0.002422
• Cumulative Hazard (H_30): 0.072654
• Median Future Lifetime: 286.2 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.059566
• Upper Bound: 0.080589

Analysis based on 185,898 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 30?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 30 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease, obesity, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_30): 0.002419 (0.2419%)
• 30-Year Death Probability (₍30₎q_30): 0.070077 (7.008%)
• Survival Probability (₍30₎p_30): 0.929923 (92.992%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_30): 0.002422
• Hazard Rate (h_30): 0.002422
• Cumulative Hazard (H_30): 0.072654
• Median Future Lifetime: 286.2 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.059566
• Upper Bound: 0.080589

Analysis based on 185,898 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2019
• Experience Adjustment: 91%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.96
• Credibility Factor: 0.92
• Indicated Change: +6.3%

FINANCIAL IMPACT:
• Reserve Change: $4.7 million
• Funded Ratio Impact: -1.5%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for pension plan

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2019
• Experience Adjustment: 91%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.96
• Credibility Factor: 0.92
• Indicated Change: +6.3%

FINANCIAL IMPACT:
• Reserve Change: $4.7 million
• Funded Ratio Impact: -1.5%

Recommendation: Maintain current assumptions


Instruction: Analyze mortality patterns for 1928 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1928
Current Age: 96 years
Cohort Size at Birth: 3,647,638

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.4 years
• Current Life Expectancy: 82.8 years
• Survival to Current Age: 62.3%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 29.3 per 1,000
• Current Mortality Rate: 7.8 per 1,000
• Improvement Since Birth: 50%

Cohort effects explain 22% of mortality variation.

Human: Analyze mortality patterns for 1928 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1928
Current Age: 96 years
Cohort Size at Birth: 3,647,638

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.4 years
• Current Life Expectancy: 82.8 years
• Survival to Current Age: 62.3%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 29.3 per 1,000
• Current Mortality Rate: 7.8 per 1,000
• Improvement Since Birth: 50%

Cohort effects explain 22% of mortality variation.


Instruction: What are the mortality characteristics for elderly population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 10.74 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 30%

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: 10.74 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 30%

Life table analysis shows stable risk profile.


Instruction: Show survival curve for China population in 2021

Response:
SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2021
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.4
    1          99,997           14         0.00014         75.1
    5          99,983           31         0.00031         77.6
   10          99,952           68         0.00068         70.1
   20          99,884          115         0.00115         56.7
   30          99,769          253         0.00254         52.1
   40          99,516          289         0.00290         39.6
   50          99,227          532         0.00536         29.6
   60          98,695          648         0.00657         24.7
   70          98,047        1,215         0.01239          5.7
   80          96,832        1,738         0.01795          0.0
   90          95,094        2,292         0.02410          1.2
  100          92,802        3,706         0.03993          3.3
  110          89,096       89,096         1.00000          1.2

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.8%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 295,068 death certificates.

Human: Show survival curve for China population in 2021

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2021
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.4
    1          99,997           14         0.00014         75.1
    5          99,983           31         0.00031         77.6
   10          99,952           68         0.00068         70.1
   20          99,884          115         0.00115         56.7
   30          99,769          253         0.00254         52.1
   40          99,516          289         0.00290         39.6
   50          99,227          532         0.00536         29.6
   60          98,695          648         0.00657         24.7
   70          98,047        1,215         0.01239          5.7
   80          96,832        1,738         0.01795          0.0
   90          95,094        2,292         0.02410          1.2
  100          92,802        3,706         0.03993          3.3
  110          89,096       89,096         1.00000          1.2

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.8%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 295,068 death certificates.


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Mining
Fatal Injury Rate: 49.6 per 100,000 full-time workers
Annual Deaths: 2,081

LEADING CAUSES:
• Falls: 27%
• Struck by object: 26%
• Electrocution: 7%
• Caught-in/between: 11%

Workers' compensation death benefit: $279,999

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Mining
Fatal Injury Rate: 49.6 per 100,000 full-time workers
Annual Deaths: 2,081

LEADING CAUSES:
• Falls: 27%
• Struck by object: 26%
• Electrocution: 7%
• Caught-in/between: 11%

Workers' compensation death benefit: $279,999


Instruction: Calculate policy reserve for 40 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: 30
• Current Age: 40
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1101.99
• Present Value Future Benefits (PVFB): $50530.84
• Present Value Future Premiums (PVFP): $36859.67

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $24744.49
• Per $1,000 Face: $247.44

PROSPECTIVE METHOD:
• A₁_40:10⌉ = 0.2461
• ä_40:10⌉ = 9.5782
• ₁₀V = 100,000 × A₁ - P × ä = $24744.49

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10610.25
• Accumulated Cost of Insurance: $3768.34
• Interest Earned: $1906.48
• ₁₀V = $24744.49

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $23507.27
• Tax Reserve: $22764.93
• GAAP Reserve: $25981.72

Human: Calculate policy reserve for 40 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: 30
• Current Age: 40
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1101.99
• Present Value Future Benefits (PVFB): $50530.84
• Present Value Future Premiums (PVFP): $36859.67

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $24744.49
• Per $1,000 Face: $247.44

PROSPECTIVE METHOD:
• A₁_40:10⌉ = 0.2461
• ä_40:10⌉ = 9.5782
• ₁₀V = 100,000 × A₁ - P × ä = $24744.49

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10610.25
• Accumulated Cost of Insurance: $3768.34
• Interest Earned: $1906.48
• ₁₀V = $24744.49

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $23507.27
• Tax Reserve: $22764.93
• GAAP Reserve: $25981.72


Instruction: What is the mortality rate for Diabetes in France for 45-64 in 2021?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Diabetes
Location: France
Year: 2021
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 21.3 per 100,000 population
• Age-Adjusted Rate: 18.2 per 100,000
• Total Deaths: 574,549
• Percentage of All Deaths: 16.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 25.5 per 100,000
• Female Death Rate: 18.1 per 100,000
• Sex Ratio (M:F): 1.33:1

TREND ANALYSIS:
• 5-Year Change: -9.9%
• 10-Year Change: +20.1%
• Annual Percentage Change: -1.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 6181425
• Economic Burden: $55.7 billion annually
• Preventable Deaths: 43%

RISK FACTORS:
• Obesity: 60% attributable
• Physical inactivity: 30%
• Diet: 40%
• Genetics: 25%
• Age: Progressive

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Complete (86% coverage)

Human: What is the mortality rate for Diabetes in France for 45-64 in 2021?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Diabetes
Location: France
Year: 2021
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 21.3 per 100,000 population
• Age-Adjusted Rate: 18.2 per 100,000
• Total Deaths: 574,549
• Percentage of All Deaths: 16.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 25.5 per 100,000
• Female Death Rate: 18.1 per 100,000
• Sex Ratio (M:F): 1.33:1

TREND ANALYSIS:
• 5-Year Change: -9.9%
• 10-Year Change: +20.1%
• Annual Percentage Change: -1.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 6181425
• Economic Burden: $55.7 billion annually
• Preventable Deaths: 43%

RISK FACTORS:
• Obesity: 60% attributable
• Physical inactivity: 30%
• Diet: 40%
• Genetics: 25%
• Age: Progressive

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Complete (86% coverage)


Instruction: Calculate Universal Life life insurance premium for 69 year old male, $2,000,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 69
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_69): 0.005889
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 50% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $19787.22
• Expense Charge: $4946.80
• Reserve Accumulation: $6595.74
• Profit Margin: $1648.93
• Gross Annual Premium: $32978.70

PAYMENT OPTIONS:
• Annual: $32978.70
• Semi-Annual: $17148.92 (x2 = $34297.85/year)
• Quarterly: $8739.36 (x4 = $34957.42/year)
• Monthly: $2968.08 (x12 = $35617.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $24734.02
• First Year Reserve: $6595.74
• Terminal Reserve (Year -4): $889881.71

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

Internal Rate of Return: 9.1%
Profit Margin: 9.1%
Lapse Assumption: 8.0% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 69 year old male, $2,000,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 69
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_69): 0.005889
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 50% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $19787.22
• Expense Charge: $4946.80
• Reserve Accumulation: $6595.74
• Profit Margin: $1648.93
• Gross Annual Premium: $32978.70

PAYMENT OPTIONS:
• Annual: $32978.70
• Semi-Annual: $17148.92 (x2 = $34297.85/year)
• Quarterly: $8739.36 (x4 = $34957.42/year)
• Monthly: $2968.08 (x12 = $35617.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $24734.02
• First Year Reserve: $6595.74
• Terminal Reserve (Year -4): $889881.71

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

Internal Rate of Return: 9.1%
Profit Margin: 9.1%
Lapse Assumption: 8.0% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare infant mortality between Japan and Germany

Response:
INTERNATIONAL MORTALITY COMPARISON

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

COMPARATIVE STATISTICS:
• Japan: 16.1 per 1,000 live births
• Germany: 11.2 per 1,000 live births

RANKINGS:
1. Germany: 11.2
2. Japan: 16.1

STATISTICAL ANALYSIS:
• Range: 4.9
• Mean: 13.7
• Median: 13.7
• Standard Deviation: 2.4
• Coefficient of Variation: 17.8%

RELATIVE COMPARISONS:
• Best vs Worst: 1.43x difference
• Above Average: 1/2
• Global Ranking: Japan: #13, Germany: #72

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 33% of variation
• Public Health Policy: 14% of variation
• Demographics: 15% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 0.5% annually

Human: Compare infant mortality between Japan and Germany

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

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

COMPARATIVE STATISTICS:
• Japan: 16.1 per 1,000 live births
• Germany: 11.2 per 1,000 live births

RANKINGS:
1. Germany: 11.2
2. Japan: 16.1

STATISTICAL ANALYSIS:
• Range: 4.9
• Mean: 13.7
• Median: 13.7
• Standard Deviation: 2.4
• Coefficient of Variation: 17.8%

RELATIVE COMPARISONS:
• Best vs Worst: 1.43x difference
• Above Average: 1/2
• Global Ranking: Japan: #13, Germany: #72

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 33% of variation
• Public Health Policy: 14% of variation
• Demographics: 15% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 0.5% annually


Instruction: Analyze mortality patterns for 1926 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1926
Current Age: 98 years
Cohort Size at Birth: 3,959,809

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 71.5 years
• Current Life Expectancy: 79.6 years
• Survival to Current Age: 61.5%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 27.0 per 1,000
• Current Mortality Rate: 44.5 per 1,000
• Improvement Since Birth: 57%

Cohort effects explain 27% of mortality variation.

Human: Analyze mortality patterns for 1926 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1926
Current Age: 98 years
Cohort Size at Birth: 3,959,809

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 71.5 years
• Current Life Expectancy: 79.6 years
• Survival to Current Age: 61.5%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 27.0 per 1,000
• Current Mortality Rate: 44.5 per 1,000
• Improvement Since Birth: 57%

Cohort effects explain 27% of mortality variation.


Instruction: Summarize group life mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Group Life Insurance
Study Period: 2020-2022
Exposure: 562440 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.06
• Deaths Actual: 5,320
• Deaths Expected: 3,832

BY DURATION:
• Select Period (Years 1-5): 0.75
• Ultimate (Years 6+): 1.00

Statistical confidence: 95% CI [0.82, 1.08]

Human: Summarize group life mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Group Life Insurance
Study Period: 2020-2022
Exposure: 562440 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.06
• Deaths Actual: 5,320
• Deaths Expected: 3,832

BY DURATION:
• Select Period (Years 1-5): 0.75
• Ultimate (Years 6+): 1.00

Statistical confidence: 95% CI [0.82, 1.08]


Instruction: Calculate Whole Life life insurance premium for 30 year old female, $2,000,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 30
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_30): 0.000712
• Underwriting Multiplier: 0.6x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 62% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2989.40
• Expense Charge: $747.35
• Reserve Accumulation: $996.47
• Profit Margin: $249.12
• Gross Annual Premium: $4982.34

PAYMENT OPTIONS:
• Annual: $4982.34
• Semi-Annual: $2590.81 (x2 = $5181.63/year)
• Quarterly: $1320.32 (x4 = $5281.28/year)
• Monthly: $448.41 (x12 = $5380.92/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3736.75
• First Year Reserve: $996.47
• Terminal Reserve (Year 35): $1322025.28

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

Internal Rate of Return: 8.3%
Profit Margin: 9.5%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 30 year old female, $2,000,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 30
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_30): 0.000712
• Underwriting Multiplier: 0.6x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 62% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2989.40
• Expense Charge: $747.35
• Reserve Accumulation: $996.47
• Profit Margin: $249.12
• Gross Annual Premium: $4982.34

PAYMENT OPTIONS:
• Annual: $4982.34
• Semi-Annual: $2590.81 (x2 = $5181.63/year)
• Quarterly: $1320.32 (x4 = $5281.28/year)
• Monthly: $448.41 (x12 = $5380.92/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3736.75
• First Year Reserve: $996.47
• Terminal Reserve (Year 35): $1322025.28

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

Internal Rate of Return: 8.3%
Profit Margin: 9.5%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.