Instruction: Calculate policy reserve for 63 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: 53
• Current Age: 63
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1201.71
• Present Value Future Benefits (PVFB): $50612.80
• Present Value Future Premiums (PVFP): $38660.20

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $24885.68
• Per $1,000 Face: $248.86

PROSPECTIVE METHOD:
• A₁_63:10⌉ = 0.1746
• ä_63:10⌉ = 8.8258
• ₁₀V = 100,000 × A₁ - P × ä = $24885.68

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11980.06
• Accumulated Cost of Insurance: $4652.05
• Interest Earned: $1955.37
• ₁₀V = $24885.68

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $23641.40
• Tax Reserve: $22894.83
• GAAP Reserve: $26129.97

Human: Calculate policy reserve for 63 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: 53
• Current Age: 63
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1201.71
• Present Value Future Benefits (PVFB): $50612.80
• Present Value Future Premiums (PVFP): $38660.20

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $24885.68
• Per $1,000 Face: $248.86

PROSPECTIVE METHOD:
• A₁_63:10⌉ = 0.1746
• ä_63:10⌉ = 8.8258
• ₁₀V = 100,000 × A₁ - P × ä = $24885.68

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11980.06
• Accumulated Cost of Insurance: $4652.05
• Interest Earned: $1955.37
• ₁₀V = $24885.68

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $23641.40
• Tax Reserve: $22894.83
• GAAP Reserve: $26129.97


Instruction: Analyze mortality trends in Japan from 2000-2024

Response:
MORTALITY TREND ANALYSIS

Country: Japan
Analysis Period: 2000-2024

OVERALL TRENDS:
• Average Annual Change: -1.1%
• Total Change: -7.6%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.1 years.
Age-standardized death rate changed by +154 per 100,000.

KEY DRIVERS:
• Medical advances: 25% of improvement
• Public health measures: 29%
• Lifestyle changes: +11%
• Environmental factors: -10%

Human: Analyze mortality trends in Japan from 2000-2024

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Japan
Analysis Period: 2000-2024

OVERALL TRENDS:
• Average Annual Change: -1.1%
• Total Change: -7.6%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.1 years.
Age-standardized death rate changed by +154 per 100,000.

KEY DRIVERS:
• Medical advances: 25% of improvement
• Public health measures: 29%
• Lifestyle changes: +11%
• Environmental factors: -10%


Instruction: Calculate Term life insurance premium for 51 year old female, $100,000 coverage, 30 year term, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $100,000
• Term Length: 30 years
• Issue Age: 51
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_51): 0.003583
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $215.00
• Expense Charge: $53.75
• Reserve Accumulation: $71.67
• Profit Margin: $17.92
• Gross Annual Premium: $358.33

PAYMENT OPTIONS:
• Annual: $358.33
• Semi-Annual: $186.33 (x2 = $372.66/year)
• Quarterly: $94.96 (x4 = $379.83/year)
• Monthly: $32.25 (x12 = $386.99/year)

RESERVE CALCULATIONS:
• Net Level Premium: $268.75
• First Year Reserve: $71.67
• Terminal Reserve (Year 30): $57736.06

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

Internal Rate of Return: 11.5%
Profit Margin: 8.9%
Lapse Assumption: 6.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 51 year old female, $100,000 coverage, 30 year term, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $100,000
• Term Length: 30 years
• Issue Age: 51
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_51): 0.003583
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $215.00
• Expense Charge: $53.75
• Reserve Accumulation: $71.67
• Profit Margin: $17.92
• Gross Annual Premium: $358.33

PAYMENT OPTIONS:
• Annual: $358.33
• Semi-Annual: $186.33 (x2 = $372.66/year)
• Quarterly: $94.96 (x4 = $379.83/year)
• Monthly: $32.25 (x12 = $386.99/year)

RESERVE CALCULATIONS:
• Net Level Premium: $268.75
• First Year Reserve: $71.67
• Terminal Reserve (Year 30): $57736.06

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

Internal Rate of Return: 11.5%
Profit Margin: 8.9%
Lapse Assumption: 6.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Show survival curve for China female in 2017

Response:
SURVIVAL CURVE ANALYSIS

Population: China Female
Reference Year: 2017
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         82.4
    1          99,997            9         0.00009         77.0
    5          99,988           26         0.00026         75.9
   10          99,962           48         0.00048         74.5
   20          99,914           87         0.00087         58.7
   30          99,827          215         0.00215         50.7
   40          99,612          309         0.00310         40.9
   50          99,303          387         0.00390         28.6
   60          98,916          544         0.00550         24.9
   70          98,372        1,120         0.01139         11.1
   80          97,252        1,646         0.01693          4.4
   90          95,606        1,930         0.02019          3.0
  100          93,676        2,407         0.02569          3.6
  110          91,269       91,269         1.00000          4.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.73

The survival curve follows Gompertz law after age 30.
Data sourced from 207,476 death certificates.

Human: Show survival curve for China female in 2017

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: China Female
Reference Year: 2017
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         82.4
    1          99,997            9         0.00009         77.0
    5          99,988           26         0.00026         75.9
   10          99,962           48         0.00048         74.5
   20          99,914           87         0.00087         58.7
   30          99,827          215         0.00215         50.7
   40          99,612          309         0.00310         40.9
   50          99,303          387         0.00390         28.6
   60          98,916          544         0.00550         24.9
   70          98,372        1,120         0.01139         11.1
   80          97,252        1,646         0.01693          4.4
   90          95,606        1,930         0.02019          3.0
  100          93,676        2,407         0.02569          3.6
  110          91,269       91,269         1.00000          4.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.73

The survival curve follows Gompertz law after age 30.
Data sourced from 207,476 death certificates.


Instruction: Show survival curve for USA female in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: USA 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         82.0
    1          99,998           11         0.00011         75.1
    5          99,987           24         0.00024         72.3
   10          99,963           53         0.00053         67.2
   20          99,910          126         0.00126         61.9
   30          99,784          215         0.00215         47.3
   40          99,569          252         0.00253         39.5
   50          99,317          541         0.00545         26.5
   60          98,776          630         0.00638         17.9
   70          98,146        1,088         0.01109         10.1
   80          97,058        1,359         0.01400          0.0
   90          95,699        2,143         0.02239          2.6
  100          93,556        3,222         0.03444          4.4
  110          90,334       90,334         1.00000          4.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• 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 430,007 death certificates.

Human: Show survival curve for USA female in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: USA 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         82.0
    1          99,998           11         0.00011         75.1
    5          99,987           24         0.00024         72.3
   10          99,963           53         0.00053         67.2
   20          99,910          126         0.00126         61.9
   30          99,784          215         0.00215         47.3
   40          99,569          252         0.00253         39.5
   50          99,317          541         0.00545         26.5
   60          98,776          630         0.00638         17.9
   70          98,146        1,088         0.01109         10.1
   80          97,058        1,359         0.01400          0.0
   90          95,699        2,143         0.02239          2.6
  100          93,556        3,222         0.03444          4.4
  110          90,334       90,334         1.00000          4.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• 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 430,007 death certificates.


Instruction: Compare infant mortality between USA, Mexico, South Korea, Japan and Spain

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: USA, Mexico, South Korea, Japan, Spain
Reference Year: 2020

COMPARATIVE STATISTICS:
• USA: 16.6 per 1,000 live births
• Mexico: 29.6 per 1,000 live births
• South Korea: 26.0 per 1,000 live births
• Japan: 2.2 per 1,000 live births
• Spain: 13.1 per 1,000 live births

RANKINGS:
1. Japan: 2.2
2. Spain: 13.1
3. USA: 16.6
4. South Korea: 26.0
5. Mexico: 29.6

STATISTICAL ANALYSIS:
• Range: 27.5
• Mean: 17.5
• Median: 16.6
• Standard Deviation: 9.7
• Coefficient of Variation: 55.7%

RELATIVE COMPARISONS:
• Best vs Worst: 13.76x difference
• Above Average: 2/5
• Global Ranking: USA: #3, Mexico: #23, South Korea: #111

CONTRIBUTING FACTORS:
• Healthcare System: 31% of variation
• Economic Development: 30% of variation
• Public Health Policy: 23% of variation
• Demographics: 17% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 0.7% annually

Human: Compare infant mortality between USA, Mexico, South Korea, Japan and Spain

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: USA, Mexico, South Korea, Japan, Spain
Reference Year: 2020

COMPARATIVE STATISTICS:
• USA: 16.6 per 1,000 live births
• Mexico: 29.6 per 1,000 live births
• South Korea: 26.0 per 1,000 live births
• Japan: 2.2 per 1,000 live births
• Spain: 13.1 per 1,000 live births

RANKINGS:
1. Japan: 2.2
2. Spain: 13.1
3. USA: 16.6
4. South Korea: 26.0
5. Mexico: 29.6

STATISTICAL ANALYSIS:
• Range: 27.5
• Mean: 17.5
• Median: 16.6
• Standard Deviation: 9.7
• Coefficient of Variation: 55.7%

RELATIVE COMPARISONS:
• Best vs Worst: 13.76x difference
• Above Average: 2/5
• Global Ranking: USA: #3, Mexico: #23, South Korea: #111

CONTRIBUTING FACTORS:
• Healthcare System: 31% of variation
• Economic Development: 30% of variation
• Public Health Policy: 23% of variation
• Demographics: 17% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 0.7% annually


Instruction: Show survival curve for Japan female in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: Japan 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         79.8
    1          99,998           12         0.00012         78.3
    5          99,986           21         0.00021         75.6
   10          99,965           48         0.00048         69.8
   20          99,917          120         0.00120         55.3
   30          99,797          157         0.00157         46.6
   40          99,640          309         0.00310         35.5
   50          99,331          412         0.00415         27.0
   60          98,919          810         0.00819         24.9
   70          98,109        1,059         0.01079          8.7
   80          97,050        1,266         0.01304          2.4
   90          95,784        2,248         0.02347          1.2
  100          93,536        2,771         0.02962          2.6
  110          90,765       90,765         1.00000          2.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.6 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.71

The survival curve follows Gompertz law after age 30.
Data sourced from 311,903 death certificates.

Human: Show survival curve for Japan female in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Japan 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         79.8
    1          99,998           12         0.00012         78.3
    5          99,986           21         0.00021         75.6
   10          99,965           48         0.00048         69.8
   20          99,917          120         0.00120         55.3
   30          99,797          157         0.00157         46.6
   40          99,640          309         0.00310         35.5
   50          99,331          412         0.00415         27.0
   60          98,919          810         0.00819         24.9
   70          98,109        1,059         0.01079          8.7
   80          97,050        1,266         0.01304          2.4
   90          95,784        2,248         0.02347          1.2
  100          93,536        2,771         0.02962          2.6
  110          90,765       90,765         1.00000          2.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.6 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.71

The survival curve follows Gompertz law after age 30.
Data sourced from 311,903 death certificates.


Instruction: What is the life expectancy for a 14 year old male in China as of 2020?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 14 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 14 (e_14): 57.0 years
• Expected Age at Death: 71.0 years
• Median Survival Time: 39.5 years
• Modal Age at Death: 66.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_14): 91.7%
• 10-Year Survival (₁₀p_14): 84.2%
• 20-Year Survival (₂₀p_14): 70.8%

MORTALITY METRICS:
• Force of Mortality (μ_14): 0.01725
• Probability of Death within 1 Year (q_14): 0.01711
• Hazard Rate: 0.01740

COMPARATIVE CONTEXT:
• Global Average at Age 14: 62.9 years
• Regional Rank: Top 24 globally
• Historical Trend: Stable

Based on 161,499 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.3%.

Human: What is the life expectancy for a 14 year old male in China as of 2020?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 14 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 14 (e_14): 57.0 years
• Expected Age at Death: 71.0 years
• Median Survival Time: 39.5 years
• Modal Age at Death: 66.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_14): 91.7%
• 10-Year Survival (₁₀p_14): 84.2%
• 20-Year Survival (₂₀p_14): 70.8%

MORTALITY METRICS:
• Force of Mortality (μ_14): 0.01725
• Probability of Death within 1 Year (q_14): 0.01711
• Hazard Rate: 0.01740

COMPARATIVE CONTEXT:
• Global Average at Age 14: 62.9 years
• Regional Rank: Top 24 globally
• Historical Trend: Stable

Based on 161,499 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.3%.


Instruction: Compare maternal mortality between Italy and Canada

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Italy, Canada
Reference Year: 2020

COMPARATIVE STATISTICS:
• Italy: 36.4 per 100,000 live births
• Canada: 44.4 per 100,000 live births

RANKINGS:
1. Italy: 36.4
2. Canada: 44.4

STATISTICAL ANALYSIS:
• Range: 8.0
• Mean: 40.4
• Median: 40.4
• Standard Deviation: 4.0
• Coefficient of Variation: 9.9%

RELATIVE COMPARISONS:
• Best vs Worst: 1.22x difference
• Above Average: 1/2
• Global Ranking: Italy: #102, Canada: #74

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 27% of variation
• Public Health Policy: 23% of variation
• Demographics: 12% of variation
• Environmental Factors: 12% of variation

Convergence/Divergence: Converging at 1.0% annually

Human: Compare maternal mortality between Italy and Canada

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Italy, Canada
Reference Year: 2020

COMPARATIVE STATISTICS:
• Italy: 36.4 per 100,000 live births
• Canada: 44.4 per 100,000 live births

RANKINGS:
1. Italy: 36.4
2. Canada: 44.4

STATISTICAL ANALYSIS:
• Range: 8.0
• Mean: 40.4
• Median: 40.4
• Standard Deviation: 4.0
• Coefficient of Variation: 9.9%

RELATIVE COMPARISONS:
• Best vs Worst: 1.22x difference
• Above Average: 1/2
• Global Ranking: Italy: #102, Canada: #74

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 27% of variation
• Public Health Policy: 23% of variation
• Demographics: 12% of variation
• Environmental Factors: 12% of variation

Convergence/Divergence: Converging at 1.0% annually


Instruction: Calculate Variable Universal Life life insurance premium for 20 year old female, $750,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• 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: 93% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $573.75
• Expense Charge: $143.44
• Reserve Accumulation: $191.25
• Profit Margin: $47.81
• Gross Annual Premium: $956.25

PAYMENT OPTIONS:
• Annual: $956.25
• Semi-Annual: $497.25 (x2 = $994.50/year)
• Quarterly: $253.41 (x4 = $1013.62/year)
• Monthly: $86.06 (x12 = $1032.75/year)

RESERVE CALCULATIONS:
• Net Level Premium: $717.19
• First Year Reserve: $191.25
• Terminal Reserve (Year 45): $359048.89

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2019
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 12.0%
Profit Margin: 13.4%
Lapse Assumption: 7.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 20 year old female, $750,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 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: 93% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $573.75
• Expense Charge: $143.44
• Reserve Accumulation: $191.25
• Profit Margin: $47.81
• Gross Annual Premium: $956.25

PAYMENT OPTIONS:
• Annual: $956.25
• Semi-Annual: $497.25 (x2 = $994.50/year)
• Quarterly: $253.41 (x4 = $1013.62/year)
• Monthly: $86.06 (x12 = $1032.75/year)

RESERVE CALCULATIONS:
• Net Level Premium: $717.19
• First Year Reserve: $191.25
• Terminal Reserve (Year 45): $359048.89

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2019
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 12.0%
Profit Margin: 13.4%
Lapse Assumption: 7.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Project mortality rates for India in 2050

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 666.9 per 100,000
• Life Expectancy: 85.1 years
• Annual Improvement: 0.88%

CONFIDENCE INTERVALS (95%):
• Lower: 566.8
• Upper: 766.9

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

Human: Project mortality rates for India in 2050

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 666.9 per 100,000
• Life Expectancy: 85.1 years
• Annual Improvement: 0.88%

CONFIDENCE INTERVALS (95%):
• Lower: 566.8
• Upper: 766.9

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


Instruction: Calculate policy reserve for 65 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: 55
• Current Age: 65
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1085.34
• Present Value Future Benefits (PVFB): $50271.89
• Present Value Future Premiums (PVFP): $25166.84

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $11142.85
• Per $1,000 Face: $111.43

PROSPECTIVE METHOD:
• A₁_65:10⌉ = 0.1767
• ä_65:10⌉ = 9.2451
• ₁₀V = 100,000 × A₁ - P × ä = $11142.85

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11512.64
• Accumulated Cost of Insurance: $3413.61
• Interest Earned: $1240.79
• ₁₀V = $11142.85

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $10585.71
• Tax Reserve: $10251.42
• GAAP Reserve: $11699.99

Human: Calculate policy reserve for 65 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: 55
• Current Age: 65
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1085.34
• Present Value Future Benefits (PVFB): $50271.89
• Present Value Future Premiums (PVFP): $25166.84

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $11142.85
• Per $1,000 Face: $111.43

PROSPECTIVE METHOD:
• A₁_65:10⌉ = 0.1767
• ä_65:10⌉ = 9.2451
• ₁₀V = 100,000 × A₁ - P × ä = $11142.85

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11512.64
• Accumulated Cost of Insurance: $3413.61
• Interest Earned: $1240.79
• ₁₀V = $11142.85

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $10585.71
• Tax Reserve: $10251.42
• GAAP Reserve: $11699.99


Instruction: Calculate Variable Universal Life life insurance premium for 46 year old female, $1,000,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 46
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_46): 0.001213
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 98% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1819.91
• Expense Charge: $454.98
• Reserve Accumulation: $606.64
• Profit Margin: $151.66
• Gross Annual Premium: $3033.18

PAYMENT OPTIONS:
• Annual: $3033.18
• Semi-Annual: $1577.26 (x2 = $3154.51/year)
• Quarterly: $803.79 (x4 = $3215.17/year)
• Monthly: $272.99 (x12 = $3275.84/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2274.89
• First Year Reserve: $606.64
• Terminal Reserve (Year 19): $432488.76

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

Internal Rate of Return: 11.3%
Profit Margin: 12.3%
Lapse Assumption: 7.8% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 46 year old female, $1,000,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 46
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_46): 0.001213
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 98% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1819.91
• Expense Charge: $454.98
• Reserve Accumulation: $606.64
• Profit Margin: $151.66
• Gross Annual Premium: $3033.18

PAYMENT OPTIONS:
• Annual: $3033.18
• Semi-Annual: $1577.26 (x2 = $3154.51/year)
• Quarterly: $803.79 (x4 = $3215.17/year)
• Monthly: $272.99 (x12 = $3275.84/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2274.89
• First Year Reserve: $606.64
• Terminal Reserve (Year 19): $432488.76

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

Internal Rate of Return: 11.3%
Profit Margin: 12.3%
Lapse Assumption: 7.8% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Variable Universal Life life insurance premium for 60 year old male, $250,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 60
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.003926
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 53% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1472.42
• Expense Charge: $368.10
• Reserve Accumulation: $490.81
• Profit Margin: $122.70
• Gross Annual Premium: $2454.03

PAYMENT OPTIONS:
• Annual: $2454.03
• Semi-Annual: $1276.10 (x2 = $2552.19/year)
• Quarterly: $650.32 (x4 = $2601.27/year)
• Monthly: $220.86 (x12 = $2650.35/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1840.52
• First Year Reserve: $490.81
• Terminal Reserve (Year 5): $169843.97

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

Internal Rate of Return: 8.6%
Profit Margin: 13.4%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 60 year old male, $250,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 60
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.003926
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 53% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1472.42
• Expense Charge: $368.10
• Reserve Accumulation: $490.81
• Profit Margin: $122.70
• Gross Annual Premium: $2454.03

PAYMENT OPTIONS:
• Annual: $2454.03
• Semi-Annual: $1276.10 (x2 = $2552.19/year)
• Quarterly: $650.32 (x4 = $2601.27/year)
• Monthly: $220.86 (x12 = $2650.35/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1840.52
• First Year Reserve: $490.81
• Terminal Reserve (Year 5): $169843.97

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

Internal Rate of Return: 8.6%
Profit Margin: 13.4%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Project mortality rates for Germany in 2050

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 365.9 per 100,000
• Life Expectancy: 83.2 years
• Annual Improvement: 1.95%

CONFIDENCE INTERVALS (95%):
• Lower: 311.0
• Upper: 420.8

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

Human: Project mortality rates for Germany in 2050

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 365.9 per 100,000
• Life Expectancy: 83.2 years
• Annual Improvement: 1.95%

CONFIDENCE INTERVALS (95%):
• Lower: 311.0
• Upper: 420.8

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


Instruction: What is the mortality rate for Parkinson's in Germany for 25-44 in 2020?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Parkinson's
Location: Germany
Year: 2020
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 7.0 per 100,000 population
• Age-Adjusted Rate: 6.3 per 100,000
• Total Deaths: 204,617
• Percentage of All Deaths: 15.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 8.4 per 100,000
• Female Death Rate: 6.0 per 100,000
• Sex Ratio (M:F): 1.26:1

TREND ANALYSIS:
• 5-Year Change: -13.4%
• 10-Year Change: +13.7%
• Annual Percentage Change: +2.2%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 5268641
• Economic Burden: $13.1 billion annually
• Preventable Deaths: 36%

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

International Classification of Diseases (ICD-10): G20
Data Quality: Complete (98% coverage)

Human: What is the mortality rate for Parkinson's in Germany for 25-44 in 2020?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Parkinson's
Location: Germany
Year: 2020
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 7.0 per 100,000 population
• Age-Adjusted Rate: 6.3 per 100,000
• Total Deaths: 204,617
• Percentage of All Deaths: 15.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 8.4 per 100,000
• Female Death Rate: 6.0 per 100,000
• Sex Ratio (M:F): 1.26:1

TREND ANALYSIS:
• 5-Year Change: -13.4%
• 10-Year Change: +13.7%
• Annual Percentage Change: +2.2%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 5268641
• Economic Burden: $13.1 billion annually
• Preventable Deaths: 36%

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

International Classification of Diseases (ICD-10): G20
Data Quality: Complete (98% coverage)


Instruction: Show survival curve for Brazil male in 2017

Response:
SURVIVAL CURVE ANALYSIS

Population: Brazil Male
Reference Year: 2017
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         80.8
    1          99,997           12         0.00012         78.5
    5          99,985           35         0.00035         70.9
   10          99,950           65         0.00065         70.5
   20          99,885          170         0.00170         58.9
   30          99,715          214         0.00215         53.8
   40          99,501          462         0.00464         38.1
   50          99,039          729         0.00736         29.6
   60          98,310          891         0.00906         18.0
   70          97,419        1,135         0.01165         14.2
   80          96,284        1,626         0.01689          0.0
   90          94,658        3,134         0.03311          4.4
  100          91,524        4,298         0.04696          3.5
  110          87,226       87,226         1.00000          2.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.0 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.3%
• Probability of Surviving to 80: 96.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.75

The survival curve follows Gompertz law after age 30.
Data sourced from 457,879 death certificates.

Human: Show survival curve for Brazil male in 2017

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Brazil Male
Reference Year: 2017
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         80.8
    1          99,997           12         0.00012         78.5
    5          99,985           35         0.00035         70.9
   10          99,950           65         0.00065         70.5
   20          99,885          170         0.00170         58.9
   30          99,715          214         0.00215         53.8
   40          99,501          462         0.00464         38.1
   50          99,039          729         0.00736         29.6
   60          98,310          891         0.00906         18.0
   70          97,419        1,135         0.01165         14.2
   80          96,284        1,626         0.01689          0.0
   90          94,658        3,134         0.03311          4.4
  100          91,524        4,298         0.04696          3.5
  110          87,226       87,226         1.00000          2.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.0 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.3%
• Probability of Surviving to 80: 96.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.75

The survival curve follows Gompertz law after age 30.
Data sourced from 457,879 death certificates.


Instruction: Calculate the 30-year death probability for a 39 year oldsmoker with heart disease

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 39 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_39): 0.001240 (0.1240%)
• 30-Year Death Probability (₍30₎q_39): 0.036529 (3.653%)
• Survival Probability (₍30₎p_39): 0.963471 (96.347%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_39): 0.001240
• Hazard Rate (h_39): 0.001240
• Cumulative Hazard (H_39): 0.037213
• Median Future Lifetime: 558.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.2x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 24%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.031050
• Upper Bound: 0.042008

Analysis based on 105,281 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 39 year oldsmoker with heart disease

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 39 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_39): 0.001240 (0.1240%)
• 30-Year Death Probability (₍30₎q_39): 0.036529 (3.653%)
• Survival Probability (₍30₎p_39): 0.963471 (96.347%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_39): 0.001240
• Hazard Rate (h_39): 0.001240
• Cumulative Hazard (H_39): 0.037213
• Median Future Lifetime: 558.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.2x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 24%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.031050
• Upper Bound: 0.042008

Analysis based on 105,281 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate Universal Life life insurance premium for 38 year old male, $100,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 38
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_38): 0.002095
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 79% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $352.03
• Expense Charge: $88.01
• Reserve Accumulation: $117.34
• Profit Margin: $29.34
• Gross Annual Premium: $586.72

PAYMENT OPTIONS:
• Annual: $586.72
• Semi-Annual: $305.10 (x2 = $610.19/year)
• Quarterly: $155.48 (x4 = $621.93/year)
• Monthly: $52.81 (x12 = $633.66/year)

RESERVE CALCULATIONS:
• Net Level Premium: $440.04
• First Year Reserve: $117.34
• Terminal Reserve (Year 27): $66223.56

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

Internal Rate of Return: 11.2%
Profit Margin: 13.7%
Lapse Assumption: 4.4% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 38 year old male, $100,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 38
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_38): 0.002095
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 79% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $352.03
• Expense Charge: $88.01
• Reserve Accumulation: $117.34
• Profit Margin: $29.34
• Gross Annual Premium: $586.72

PAYMENT OPTIONS:
• Annual: $586.72
• Semi-Annual: $305.10 (x2 = $610.19/year)
• Quarterly: $155.48 (x4 = $621.93/year)
• Monthly: $52.81 (x12 = $633.66/year)

RESERVE CALCULATIONS:
• Net Level Premium: $440.04
• First Year Reserve: $117.34
• Terminal Reserve (Year 27): $66223.56

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

Internal Rate of Return: 11.2%
Profit Margin: 13.7%
Lapse Assumption: 4.4% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Universal Life life insurance premium for 35 year old male, $1,000,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 35
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_35): 0.001422
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 65% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2389.00
• Expense Charge: $597.25
• Reserve Accumulation: $796.33
• Profit Margin: $199.08
• Gross Annual Premium: $3981.66

PAYMENT OPTIONS:
• Annual: $3981.66
• Semi-Annual: $2070.46 (x2 = $4140.93/year)
• Quarterly: $1055.14 (x4 = $4220.56/year)
• Monthly: $358.35 (x12 = $4300.19/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2986.25
• First Year Reserve: $796.33
• Terminal Reserve (Year 30): $499678.74

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

Internal Rate of Return: 11.4%
Profit Margin: 14.4%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 35 year old male, $1,000,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 35
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_35): 0.001422
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 65% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2389.00
• Expense Charge: $597.25
• Reserve Accumulation: $796.33
• Profit Margin: $199.08
• Gross Annual Premium: $3981.66

PAYMENT OPTIONS:
• Annual: $3981.66
• Semi-Annual: $2070.46 (x2 = $4140.93/year)
• Quarterly: $1055.14 (x4 = $4220.56/year)
• Monthly: $358.35 (x12 = $4300.19/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2986.25
• First Year Reserve: $796.33
• Terminal Reserve (Year 30): $499678.74

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

Internal Rate of Return: 11.4%
Profit Margin: 14.4%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


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

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

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

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 55 (e_55): 21.8 years
• Expected Age at Death: 76.8 years
• Median Survival Time: 15.1 years
• Modal Age at Death: 71.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_55): 80.3%
• 10-Year Survival (₁₀p_55): 64.5%
• 20-Year Survival (₂₀p_55): 41.6%

MORTALITY METRICS:
• Force of Mortality (μ_55): 0.04384
• Probability of Death within 1 Year (q_55): 0.04289
• Hazard Rate: 0.04483

COMPARATIVE CONTEXT:
• Global Average at Age 55: 23.9 years
• Regional Rank: Top 23 globally
• Historical Trend: Improving

Based on 464,000 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.0%.

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

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

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

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 55 (e_55): 21.8 years
• Expected Age at Death: 76.8 years
• Median Survival Time: 15.1 years
• Modal Age at Death: 71.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_55): 80.3%
• 10-Year Survival (₁₀p_55): 64.5%
• 20-Year Survival (₂₀p_55): 41.6%

MORTALITY METRICS:
• Force of Mortality (μ_55): 0.04384
• Probability of Death within 1 Year (q_55): 0.04289
• Hazard Rate: 0.04483

COMPARATIVE CONTEXT:
• Global Average at Age 55: 23.9 years
• Regional Rank: Top 23 globally
• Historical Trend: Improving

Based on 464,000 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.0%.


Instruction: Calculate the 30-year death probability for a 27 year oldsmoker

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 27 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_27): 0.000541 (0.0541%)
• 30-Year Death Probability (₍30₎q_27): 0.016095 (1.609%)
• Survival Probability (₍30₎p_27): 0.983905 (98.391%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_27): 0.000541
• Hazard Rate (h_27): 0.000541
• Cumulative Hazard (H_27): 0.016226
• Median Future Lifetime: 1281.6 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.013681
• Upper Bound: 0.018509

Analysis based on 141,025 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 27 year oldsmoker

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 27 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_27): 0.000541 (0.0541%)
• 30-Year Death Probability (₍30₎q_27): 0.016095 (1.609%)
• Survival Probability (₍30₎p_27): 0.983905 (98.391%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_27): 0.000541
• Hazard Rate (h_27): 0.000541
• Cumulative Hazard (H_27): 0.016226
• Median Future Lifetime: 1281.6 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.013681
• Upper Bound: 0.018509

Analysis based on 141,025 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 70 year old female in Canada as of 2023?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 70 years
• Sex: Female
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 70 (e_70): 17.7 years
• Expected Age at Death: 87.7 years
• Median Survival Time: 12.3 years
• Modal Age at Death: 82.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_70): 76.5%
• 10-Year Survival (₁₀p_70): 58.6%
• 20-Year Survival (₂₀p_70): 34.3%

MORTALITY METRICS:
• Force of Mortality (μ_70): 0.05351
• Probability of Death within 1 Year (q_70): 0.05211
• Hazard Rate: 0.05500

COMPARATIVE CONTEXT:
• Global Average at Age 70: 12.1 years
• Regional Rank: Top 14 globally
• Historical Trend: Stable

Based on 463,730 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.4%.

Human: What is the life expectancy for a 70 year old female in Canada as of 2023?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 70 years
• Sex: Female
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 70 (e_70): 17.7 years
• Expected Age at Death: 87.7 years
• Median Survival Time: 12.3 years
• Modal Age at Death: 82.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_70): 76.5%
• 10-Year Survival (₁₀p_70): 58.6%
• 20-Year Survival (₂₀p_70): 34.3%

MORTALITY METRICS:
• Force of Mortality (μ_70): 0.05351
• Probability of Death within 1 Year (q_70): 0.05211
• Hazard Rate: 0.05500

COMPARATIVE CONTEXT:
• Global Average at Age 70: 12.1 years
• Regional Rank: Top 14 globally
• Historical Trend: Stable

Based on 463,730 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.4%.


Instruction: Calculate Term life insurance premium for 43 year old female, $250,000 coverage, 15 year term, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 43
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_43): 0.002745
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $411.68
• Expense Charge: $102.92
• Reserve Accumulation: $137.23
• Profit Margin: $34.31
• Gross Annual Premium: $686.13

PAYMENT OPTIONS:
• Annual: $686.13
• Semi-Annual: $356.79 (x2 = $713.58/year)
• Quarterly: $181.83 (x4 = $727.30/year)
• Monthly: $61.75 (x12 = $741.03/year)

RESERVE CALCULATIONS:
• Net Level Premium: $514.60
• First Year Reserve: $137.23
• Terminal Reserve (Year 15): $85492.33

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

Internal Rate of Return: 8.3%
Profit Margin: 12.7%
Lapse Assumption: 5.7% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 43 year old female, $250,000 coverage, 15 year term, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 43
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_43): 0.002745
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $411.68
• Expense Charge: $102.92
• Reserve Accumulation: $137.23
• Profit Margin: $34.31
• Gross Annual Premium: $686.13

PAYMENT OPTIONS:
• Annual: $686.13
• Semi-Annual: $356.79 (x2 = $713.58/year)
• Quarterly: $181.83 (x4 = $727.30/year)
• Monthly: $61.75 (x12 = $741.03/year)

RESERVE CALCULATIONS:
• Net Level Premium: $514.60
• First Year Reserve: $137.23
• Terminal Reserve (Year 15): $85492.33

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

Internal Rate of Return: 8.3%
Profit Margin: 12.7%
Lapse Assumption: 5.7% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Whole Life life insurance premium for 65 year old male, $250,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 65
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_65): 0.003865
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2029.36
• Expense Charge: $507.34
• Reserve Accumulation: $676.45
• Profit Margin: $169.11
• Gross Annual Premium: $3382.27

PAYMENT OPTIONS:
• Annual: $3382.27
• Semi-Annual: $1758.78 (x2 = $3517.57/year)
• Quarterly: $896.30 (x4 = $3585.21/year)
• Monthly: $304.40 (x12 = $3652.86/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2536.71
• First Year Reserve: $676.45
• Terminal Reserve (Year 0): $103974.99

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

Internal Rate of Return: 10.6%
Profit Margin: 13.9%
Lapse Assumption: 3.8% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 65 year old male, $250,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 65
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_65): 0.003865
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2029.36
• Expense Charge: $507.34
• Reserve Accumulation: $676.45
• Profit Margin: $169.11
• Gross Annual Premium: $3382.27

PAYMENT OPTIONS:
• Annual: $3382.27
• Semi-Annual: $1758.78 (x2 = $3517.57/year)
• Quarterly: $896.30 (x4 = $3585.21/year)
• Monthly: $304.40 (x12 = $3652.86/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2536.71
• First Year Reserve: $676.45
• Terminal Reserve (Year 0): $103974.99

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

Internal Rate of Return: 10.6%
Profit Margin: 13.9%
Lapse Assumption: 3.8% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality differences by race in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2019

MORTALITY RATES BY RACE (per 100,000):
• White: 210.5
• Black: 606.9
• Asian: 393.2
• Hispanic: 717.8
• Native American: 513.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.70
• Rate Difference: 240.4 per 100,000
• Population Attributable Risk: 31.2%
• Gini Coefficient: 0.308

LIFE EXPECTANCY BY RACE:
• White: 79.2 years
• Black: 74.6 years
• Asian: 71.5 years
• Hispanic: 74.1 years
• Native American: 84.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 37% of disparity
• Socioeconomic Status: 27% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.7%

Social determinants explain 61% 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: 2019

MORTALITY RATES BY RACE (per 100,000):
• White: 210.5
• Black: 606.9
• Asian: 393.2
• Hispanic: 717.8
• Native American: 513.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.70
• Rate Difference: 240.4 per 100,000
• Population Attributable Risk: 31.2%
• Gini Coefficient: 0.308

LIFE EXPECTANCY BY RACE:
• White: 79.2 years
• Black: 74.6 years
• Asian: 71.5 years
• Hispanic: 74.1 years
• Native American: 84.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 37% of disparity
• Socioeconomic Status: 27% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.7%

Social determinants explain 61% of observed mortality differences.


Instruction: Calculate policy reserve for 57 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: 47
• Current Age: 57
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $974.74
• Present Value Future Benefits (PVFB): $43323.34
• Present Value Future Premiums (PVFP): $31695.35

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $39463.28
• Per $1,000 Face: $394.63

PROSPECTIVE METHOD:
• A₁_57:10⌉ = 0.1930
• ä_57:10⌉ = 8.4182
• ₁₀V = 100,000 × A₁ - P × ä = $39463.28

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9326.90
• Accumulated Cost of Insurance: $4077.11
• Interest Earned: $1918.22
• ₁₀V = $39463.28

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $37490.12
• Tax Reserve: $36306.22
• GAAP Reserve: $41436.45

Human: Calculate policy reserve for 57 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: 47
• Current Age: 57
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $974.74
• Present Value Future Benefits (PVFB): $43323.34
• Present Value Future Premiums (PVFP): $31695.35

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $39463.28
• Per $1,000 Face: $394.63

PROSPECTIVE METHOD:
• A₁_57:10⌉ = 0.1930
• ä_57:10⌉ = 8.4182
• ₁₀V = 100,000 × A₁ - P × ä = $39463.28

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9326.90
• Accumulated Cost of Insurance: $4077.11
• Interest Earned: $1918.22
• ₁₀V = $39463.28

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $37490.12
• Tax Reserve: $36306.22
• GAAP Reserve: $41436.45


Instruction: Analyze mortality patterns for 1941 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1941
Current Age: 83 years
Cohort Size at Birth: 3,494,953

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 65.4 years
• Current Life Expectancy: 76.6 years
• Survival to Current Age: 82.2%

HISTORICAL EXPOSURES:
• World War II

MORTALITY PATTERN:
• Peak Infant Mortality: 24.9 per 1,000
• Current Mortality Rate: 41.6 per 1,000
• Improvement Since Birth: 44%

Cohort effects explain 27% of mortality variation.

Human: Analyze mortality patterns for 1941 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1941
Current Age: 83 years
Cohort Size at Birth: 3,494,953

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 65.4 years
• Current Life Expectancy: 76.6 years
• Survival to Current Age: 82.2%

HISTORICAL EXPOSURES:
• World War II

MORTALITY PATTERN:
• Peak Infant Mortality: 24.9 per 1,000
• Current Mortality Rate: 41.6 per 1,000
• Improvement Since Birth: 44%

Cohort effects explain 27% of mortality variation.


Instruction: Calculate Variable Universal Life life insurance premium for 29 year old female, $750,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 29
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_29): 0.001721
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 99% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1936.20
• Expense Charge: $484.05
• Reserve Accumulation: $645.40
• Profit Margin: $161.35
• Gross Annual Premium: $3227.01

PAYMENT OPTIONS:
• Annual: $3227.01
• Semi-Annual: $1678.04 (x2 = $3356.09/year)
• Quarterly: $855.16 (x4 = $3420.63/year)
• Monthly: $290.43 (x12 = $3485.17/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2420.25
• First Year Reserve: $645.40
• Terminal Reserve (Year 36): $416472.20

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

Internal Rate of Return: 10.4%
Profit Margin: 14.6%
Lapse Assumption: 5.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 29 year old female, $750,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 29
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_29): 0.001721
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 99% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1936.20
• Expense Charge: $484.05
• Reserve Accumulation: $645.40
• Profit Margin: $161.35
• Gross Annual Premium: $3227.01

PAYMENT OPTIONS:
• Annual: $3227.01
• Semi-Annual: $1678.04 (x2 = $3356.09/year)
• Quarterly: $855.16 (x4 = $3420.63/year)
• Monthly: $290.43 (x12 = $3485.17/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2420.25
• First Year Reserve: $645.40
• Terminal Reserve (Year 36): $416472.20

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

Internal Rate of Return: 10.4%
Profit Margin: 14.6%
Lapse Assumption: 5.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate excess mortality during 2022 heat wave in Brazil for Q4 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Brazil
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 74,390
• Observed Deaths: 103,603
• Excess Deaths: 29,213
• Excess Mortality Rate: 39.3%
• P-score: 39.3%
• Z-score: 3.61 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.9% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.2% (2,921 deaths)
• 45-64 years: 5.3% (7,303 deaths)
• 65-74 years: 26.6% (7,303 deaths)
• 75+ years: 18.8% (11,685 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 16,354 (57%)
• Indirect (probable): 6,152 (10%)
• Collateral (delayed care): 5,145 (11%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [24,831, 33,594]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 308443
Economic Impact: $10.0 billion
Quality-Adjusted Life Years Lost: 252334

Human: Calculate excess mortality during 2022 heat wave in Brazil for Q4 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Brazil
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 74,390
• Observed Deaths: 103,603
• Excess Deaths: 29,213
• Excess Mortality Rate: 39.3%
• P-score: 39.3%
• Z-score: 3.61 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.9% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.2% (2,921 deaths)
• 45-64 years: 5.3% (7,303 deaths)
• 65-74 years: 26.6% (7,303 deaths)
• 75+ years: 18.8% (11,685 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 16,354 (57%)
• Indirect (probable): 6,152 (10%)
• Collateral (delayed care): 5,145 (11%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [24,831, 33,594]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 308443
Economic Impact: $10.0 billion
Quality-Adjusted Life Years Lost: 252334


Instruction: Compare cancer mortality between Italy and Russia

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Italy, Russia
Reference Year: 2022

COMPARATIVE STATISTICS:
• Italy: 149.5 per 100,000 population
• Russia: 249.1 per 100,000 population

RANKINGS:
1. Italy: 149.5
2. Russia: 249.1

STATISTICAL ANALYSIS:
• Range: 99.6
• Mean: 199.3
• Median: 199.3
• Standard Deviation: 49.8
• Coefficient of Variation: 25.0%

RELATIVE COMPARISONS:
• Best vs Worst: 1.67x difference
• Above Average: 1/2
• Global Ranking: Italy: #139, Russia: #100

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 24% of variation
• Public Health Policy: 16% of variation
• Demographics: 18% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.4% annually

Human: Compare cancer mortality between Italy and Russia

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Italy, Russia
Reference Year: 2022

COMPARATIVE STATISTICS:
• Italy: 149.5 per 100,000 population
• Russia: 249.1 per 100,000 population

RANKINGS:
1. Italy: 149.5
2. Russia: 249.1

STATISTICAL ANALYSIS:
• Range: 99.6
• Mean: 199.3
• Median: 199.3
• Standard Deviation: 49.8
• Coefficient of Variation: 25.0%

RELATIVE COMPARISONS:
• Best vs Worst: 1.67x difference
• Above Average: 1/2
• Global Ranking: Italy: #139, Russia: #100

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 24% of variation
• Public Health Policy: 16% of variation
• Demographics: 18% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.4% annually


Instruction: Analyze mortality trends in Germany from 2002-2020

Response:
MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2002-2020

OVERALL TRENDS:
• Average Annual Change: -0.7%
• Total Change: +8.6%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.1 years.
Age-standardized death rate changed by +79 per 100,000.

KEY DRIVERS:
• Medical advances: 20% of improvement
• Public health measures: 30%
• Lifestyle changes: -14%
• Environmental factors: -5%

Human: Analyze mortality trends in Germany from 2002-2020

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2002-2020

OVERALL TRENDS:
• Average Annual Change: -0.7%
• Total Change: +8.6%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.1 years.
Age-standardized death rate changed by +79 per 100,000.

KEY DRIVERS:
• Medical advances: 20% of improvement
• Public health measures: 30%
• Lifestyle changes: -14%
• Environmental factors: -5%


Instruction: Project mortality rates for India in 2033

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 646.8 per 100,000
• Life Expectancy: 81.6 years
• Annual Improvement: 1.53%

CONFIDENCE INTERVALS (95%):
• Lower: 549.8
• Upper: 743.9

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

Human: Project mortality rates for India in 2033

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 646.8 per 100,000
• Life Expectancy: 81.6 years
• Annual Improvement: 1.53%

CONFIDENCE INTERVALS (95%):
• Lower: 549.8
• Upper: 743.9

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


Instruction: What is the mortality rate for Stroke in France for 45-64 in 2023?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Stroke
Location: France
Year: 2023
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 27.5 per 100,000 population
• Age-Adjusted Rate: 24.2 per 100,000
• Total Deaths: 209,180
• Percentage of All Deaths: 12.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 33.0 per 100,000
• Female Death Rate: 23.4 per 100,000
• Sex Ratio (M:F): 1.33:1

TREND ANALYSIS:
• 5-Year Change: -12.8%
• 10-Year Change: -6.4%
• Annual Percentage Change: +1.5%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 4521419
• Economic Burden: $10.6 billion annually
• Preventable Deaths: 20%

RISK FACTORS:
• Hypertension: 50% attributable
• Atrial fibrillation: 25%
• Diabetes: 20%
• High cholesterol: 15%
• Smoking: 20%

International Classification of Diseases (ICD-10): I60-I69
Data Quality: Complete (86% coverage)

Human: What is the mortality rate for Stroke in France for 45-64 in 2023?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Stroke
Location: France
Year: 2023
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 27.5 per 100,000 population
• Age-Adjusted Rate: 24.2 per 100,000
• Total Deaths: 209,180
• Percentage of All Deaths: 12.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 33.0 per 100,000
• Female Death Rate: 23.4 per 100,000
• Sex Ratio (M:F): 1.33:1

TREND ANALYSIS:
• 5-Year Change: -12.8%
• 10-Year Change: -6.4%
• Annual Percentage Change: +1.5%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 4521419
• Economic Burden: $10.6 billion annually
• Preventable Deaths: 20%

RISK FACTORS:
• Hypertension: 50% attributable
• Atrial fibrillation: 25%
• Diabetes: 20%
• High cholesterol: 15%
• Smoking: 20%

International Classification of Diseases (ICD-10): I60-I69
Data Quality: Complete (86% coverage)


Instruction: What is the life expectancy for a 81 year old female in USA as of 2019?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 81 years
• Sex: Female
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 81 (e_81): 4.0 years
• Expected Age at Death: 85.0 years
• Median Survival Time: 2.8 years
• Modal Age at Death: 80.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_81): 36.9%
• 10-Year Survival (₁₀p_81): 13.6%
• 20-Year Survival (₂₀p_81): 1.8%

MORTALITY METRICS:
• Force of Mortality (μ_81): 0.19955
• Probability of Death within 1 Year (q_81): 0.18090
• Hazard Rate: 0.22259

COMPARATIVE CONTEXT:
• Global Average at Age 81: -2.1 years
• Regional Rank: Top 16 globally
• Historical Trend: Stable

Based on 183,913 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.6%.

Human: What is the life expectancy for a 81 year old female in USA as of 2019?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 81 years
• Sex: Female
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 81 (e_81): 4.0 years
• Expected Age at Death: 85.0 years
• Median Survival Time: 2.8 years
• Modal Age at Death: 80.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_81): 36.9%
• 10-Year Survival (₁₀p_81): 13.6%
• 20-Year Survival (₂₀p_81): 1.8%

MORTALITY METRICS:
• Force of Mortality (μ_81): 0.19955
• Probability of Death within 1 Year (q_81): 0.18090
• Hazard Rate: 0.22259

COMPARATIVE CONTEXT:
• Global Average at Age 81: -2.1 years
• Regional Rank: Top 16 globally
• Historical Trend: Stable

Based on 183,913 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.6%.


Instruction: Compare rural vs other area mortality rates in Australia

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: Australia
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 883.1
• Rural: 1049.1
• Suburban: 817.9

Rural areas show 18.8% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare rural vs other area mortality rates in Australia

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: Australia
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 883.1
• Rural: 1049.1
• Suburban: 817.9

Rural areas show 18.8% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Compare maternal mortality between France and China

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: France, China
Reference Year: 2020

COMPARATIVE STATISTICS:
• France: 35.4 per 100,000 live births
• China: 28.6 per 100,000 live births

RANKINGS:
1. China: 28.6
2. France: 35.4

STATISTICAL ANALYSIS:
• Range: 6.7
• Mean: 32.0
• Median: 32.0
• Standard Deviation: 3.4
• Coefficient of Variation: 10.5%

RELATIVE COMPARISONS:
• Best vs Worst: 1.24x difference
• Above Average: 1/2
• Global Ranking: France: #125, China: #157

CONTRIBUTING FACTORS:
• Healthcare System: 26% of variation
• Economic Development: 34% of variation
• Public Health Policy: 19% of variation
• Demographics: 19% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.9% annually

Human: Compare maternal mortality between France and China

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: France, China
Reference Year: 2020

COMPARATIVE STATISTICS:
• France: 35.4 per 100,000 live births
• China: 28.6 per 100,000 live births

RANKINGS:
1. China: 28.6
2. France: 35.4

STATISTICAL ANALYSIS:
• Range: 6.7
• Mean: 32.0
• Median: 32.0
• Standard Deviation: 3.4
• Coefficient of Variation: 10.5%

RELATIVE COMPARISONS:
• Best vs Worst: 1.24x difference
• Above Average: 1/2
• Global Ranking: France: #125, China: #157

CONTRIBUTING FACTORS:
• Healthcare System: 26% of variation
• Economic Development: 34% of variation
• Public Health Policy: 19% of variation
• Demographics: 19% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Converging at 1.9% annually


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

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

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

MORTALITY STATISTICS:
• Crude Death Rate: 31.6 per 100,000 population
• Age-Adjusted Rate: 27.7 per 100,000
• Total Deaths: 645,805
• Percentage of All Deaths: 7.5%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 37.9 per 100,000
• Female Death Rate: 26.9 per 100,000
• Sex Ratio (M:F): 1.23:1

TREND ANALYSIS:
• 5-Year Change: -11.0%
• 10-Year Change: +15.6%
• Annual Percentage Change: -1.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #13
• Years of Potential Life Lost (YPLL): 15083482
• Economic Burden: $40.6 billion annually
• Preventable Deaths: 40%

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

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Near-Complete (98% coverage)

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

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

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

MORTALITY STATISTICS:
• Crude Death Rate: 31.6 per 100,000 population
• Age-Adjusted Rate: 27.7 per 100,000
• Total Deaths: 645,805
• Percentage of All Deaths: 7.5%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 37.9 per 100,000
• Female Death Rate: 26.9 per 100,000
• Sex Ratio (M:F): 1.23:1

TREND ANALYSIS:
• 5-Year Change: -11.0%
• 10-Year Change: +15.6%
• Annual Percentage Change: -1.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #13
• Years of Potential Life Lost (YPLL): 15083482
• Economic Burden: $40.6 billion annually
• Preventable Deaths: 40%

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

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Near-Complete (98% coverage)


Instruction: Mortality risk assessment for 48 year old over next 5 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 48 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_48): 0.001692 (0.1692%)
• 5-Year Death Probability (₍5₎q_48): 0.008430 (0.843%)
• Survival Probability (₍5₎p_48): 0.991570 (99.157%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_48): 0.001693
• Hazard Rate (h_48): 0.001693
• Cumulative Hazard (H_48): 0.008466
• Median Future Lifetime: 409.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.7x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 69%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007166
• Upper Bound: 0.009695

Analysis based on 98,166 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 48 year old over next 5 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 48 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_48): 0.001692 (0.1692%)
• 5-Year Death Probability (₍5₎q_48): 0.008430 (0.843%)
• Survival Probability (₍5₎p_48): 0.991570 (99.157%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_48): 0.001693
• Hazard Rate (h_48): 0.001693
• Cumulative Hazard (H_48): 0.008466
• Median Future Lifetime: 409.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.7x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 69%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007166
• Upper Bound: 0.009695

Analysis based on 98,166 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 52 year old male in Japan as of 2018?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 52 years
• Sex: Male
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 52 (e_52): 32.1 years
• Expected Age at Death: 84.1 years
• Median Survival Time: 22.2 years
• Modal Age at Death: 79.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_52): 86.0%
• 10-Year Survival (₁₀p_52): 73.9%
• 20-Year Survival (₂₀p_52): 54.6%

MORTALITY METRICS:
• Force of Mortality (μ_52): 0.03021
• Probability of Death within 1 Year (q_52): 0.02976
• Hazard Rate: 0.03068

COMPARATIVE CONTEXT:
• Global Average at Age 52: 32.6 years
• Regional Rank: Top 12 globally
• Historical Trend: Improving

Based on 499,180 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.8%.

Human: What is the life expectancy for a 52 year old male in Japan as of 2018?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 52 years
• Sex: Male
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 52 (e_52): 32.1 years
• Expected Age at Death: 84.1 years
• Median Survival Time: 22.2 years
• Modal Age at Death: 79.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_52): 86.0%
• 10-Year Survival (₁₀p_52): 73.9%
• 20-Year Survival (₂₀p_52): 54.6%

MORTALITY METRICS:
• Force of Mortality (μ_52): 0.03021
• Probability of Death within 1 Year (q_52): 0.02976
• Hazard Rate: 0.03068

COMPARATIVE CONTEXT:
• Global Average at Age 52: 32.6 years
• Regional Rank: Top 12 globally
• Historical Trend: Improving

Based on 499,180 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.8%.


Instruction: What is the mortality rate for Alzheimer's in UK for Under 25 in 2021?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Alzheimer's
Location: UK
Year: 2021
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 28.4 per 100,000 population
• Age-Adjusted Rate: 25.0 per 100,000
• Total Deaths: 135,928
• Percentage of All Deaths: 3.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 34.1 per 100,000
• Female Death Rate: 24.1 per 100,000
• Sex Ratio (M:F): 1.21:1

TREND ANALYSIS:
• 5-Year Change: +10.2%
• 10-Year Change: -6.5%
• Annual Percentage Change: +1.9%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 3524240
• Economic Burden: $90.3 billion annually
• Preventable Deaths: 60%

RISK FACTORS:
• Age: Primary factor
• Genetics (APOE4): 25%
• Education level: -15%
• Cardiovascular health: 20%
• Head trauma: 10%

International Classification of Diseases (ICD-10): G30
Data Quality: Complete (99% coverage)

Human: What is the mortality rate for Alzheimer's in UK for Under 25 in 2021?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Alzheimer's
Location: UK
Year: 2021
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 28.4 per 100,000 population
• Age-Adjusted Rate: 25.0 per 100,000
• Total Deaths: 135,928
• Percentage of All Deaths: 3.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 34.1 per 100,000
• Female Death Rate: 24.1 per 100,000
• Sex Ratio (M:F): 1.21:1

TREND ANALYSIS:
• 5-Year Change: +10.2%
• 10-Year Change: -6.5%
• Annual Percentage Change: +1.9%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 3524240
• Economic Burden: $90.3 billion annually
• Preventable Deaths: 60%

RISK FACTORS:
• Age: Primary factor
• Genetics (APOE4): 25%
• Education level: -15%
• Cardiovascular health: 20%
• Head trauma: 10%

International Classification of Diseases (ICD-10): G30
Data Quality: Complete (99% coverage)


Instruction: Compare cardiovascular mortality between France and South Korea

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: France, South Korea
Reference Year: 2020

COMPARATIVE STATISTICS:
• France: 83.0 per 100,000 population
• South Korea: 101.3 per 100,000 population

RANKINGS:
1. France: 83.0
2. South Korea: 101.3

STATISTICAL ANALYSIS:
• Range: 18.3
• Mean: 92.1
• Median: 92.1
• Standard Deviation: 9.1
• Coefficient of Variation: 9.9%

RELATIVE COMPARISONS:
• Best vs Worst: 1.22x difference
• Above Average: 1/2
• Global Ranking: France: #104, South Korea: #169

CONTRIBUTING FACTORS:
• Healthcare System: 23% of variation
• Economic Development: 16% of variation
• Public Health Policy: 15% of variation
• Demographics: 16% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 2.0% annually

Human: Compare cardiovascular mortality between France and South Korea

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: France, South Korea
Reference Year: 2020

COMPARATIVE STATISTICS:
• France: 83.0 per 100,000 population
• South Korea: 101.3 per 100,000 population

RANKINGS:
1. France: 83.0
2. South Korea: 101.3

STATISTICAL ANALYSIS:
• Range: 18.3
• Mean: 92.1
• Median: 92.1
• Standard Deviation: 9.1
• Coefficient of Variation: 9.9%

RELATIVE COMPARISONS:
• Best vs Worst: 1.22x difference
• Above Average: 1/2
• Global Ranking: France: #104, South Korea: #169

CONTRIBUTING FACTORS:
• Healthcare System: 23% of variation
• Economic Development: 16% of variation
• Public Health Policy: 15% of variation
• Demographics: 16% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 2.0% annually


Instruction: Calculate mortality improvement factors for age 60

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 60
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.76%
• Current (2024): 0.59%
• Ultimate (2044+): 0.54%

PROJECTION FACTORS:
• 10-Year Factor: 0.9423
• 20-Year Factor: 0.8879
• 30-Year Factor: 0.8367

Cohort effect adjustment: Applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 60

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 60
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.76%
• Current (2024): 0.59%
• Ultimate (2044+): 0.54%

PROJECTION FACTORS:
• 10-Year Factor: 0.9423
• 20-Year Factor: 0.8879
• 30-Year Factor: 0.8367

Cohort effect adjustment: Applied
Gender-specific: No


Instruction: What is the life expectancy for a 95 year old both in France as of 2015?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 95 years
• Sex: Both
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 95 (e_95): 0.0 years
• Expected Age at Death: 95.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 90.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_95): 0.7%
• 10-Year Survival (₁₀p_95): 0.0%
• 20-Year Survival (₂₀p_95): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_95): 1.00000
• Probability of Death within 1 Year (q_95): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 95: -12.5 years
• Regional Rank: Top 3 globally
• Historical Trend: Improving

Based on 350,876 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.

Human: What is the life expectancy for a 95 year old both in France as of 2015?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 95 years
• Sex: Both
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 95 (e_95): 0.0 years
• Expected Age at Death: 95.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 90.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_95): 0.7%
• 10-Year Survival (₁₀p_95): 0.0%
• 20-Year Survival (₂₀p_95): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_95): 1.00000
• Probability of Death within 1 Year (q_95): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 95: -12.5 years
• Regional Rank: Top 3 globally
• Historical Trend: Improving

Based on 350,876 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.


Instruction: Mortality risk assessment for 68 year old over next 5 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 68 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_68): 0.001745 (0.1745%)
• 5-Year Death Probability (₍5₎q_68): 0.008693 (0.869%)
• Survival Probability (₍5₎p_68): 0.991307 (99.131%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_68): 0.001746
• Hazard Rate (h_68): 0.001746
• Cumulative Hazard (H_68): 0.008731
• Median Future Lifetime: 396.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.7x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 74%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007389
• Upper Bound: 0.009997

Analysis based on 161,227 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 68 year old over next 5 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 68 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_68): 0.001745 (0.1745%)
• 5-Year Death Probability (₍5₎q_68): 0.008693 (0.869%)
• Survival Probability (₍5₎p_68): 0.991307 (99.131%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_68): 0.001746
• Hazard Rate (h_68): 0.001746
• Cumulative Hazard (H_68): 0.008731
• Median Future Lifetime: 396.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.7x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 74%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.007389
• Upper Bound: 0.009997

Analysis based on 161,227 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the mortality rate for Kidney Disease in Germany for 65-74 in 2023?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Kidney Disease
Location: Germany
Year: 2023
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 9.5 per 100,000 population
• Age-Adjusted Rate: 8.8 per 100,000
• Total Deaths: 347,875
• Percentage of All Deaths: 11.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 11.4 per 100,000
• Female Death Rate: 8.1 per 100,000
• Sex Ratio (M:F): 1.29:1

TREND ANALYSIS:
• 5-Year Change: +5.2%
• 10-Year Change: -21.4%
• Annual Percentage Change: -2.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #11
• Years of Potential Life Lost (YPLL): 8916554
• Economic Burden: $65.0 billion annually
• Preventable Deaths: 32%

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

International Classification of Diseases (ICD-10): N00-N19
Data Quality: Complete (96% coverage)

Human: What is the mortality rate for Kidney Disease in Germany for 65-74 in 2023?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Kidney Disease
Location: Germany
Year: 2023
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 9.5 per 100,000 population
• Age-Adjusted Rate: 8.8 per 100,000
• Total Deaths: 347,875
• Percentage of All Deaths: 11.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 11.4 per 100,000
• Female Death Rate: 8.1 per 100,000
• Sex Ratio (M:F): 1.29:1

TREND ANALYSIS:
• 5-Year Change: +5.2%
• 10-Year Change: -21.4%
• Annual Percentage Change: -2.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #11
• Years of Potential Life Lost (YPLL): 8916554
• Economic Burden: $65.0 billion annually
• Preventable Deaths: 32%

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

International Classification of Diseases (ICD-10): N00-N19
Data Quality: Complete (96% coverage)


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

Response:
EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Spain
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 20,959
• Observed Deaths: 28,732
• Excess Deaths: 7,773
• Excess Mortality Rate: 37.1%
• P-score: 37.1%
• Z-score: 5.96 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -3.8% (777 deaths)
• 45-64 years: 12.7% (1,943 deaths)
• 65-74 years: 27.0% (1,943 deaths)
• 75+ years: 20.1% (3,109 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 6,116 (58%)
• Indirect (probable): 1,897 (23%)
• Collateral (delayed care): 1,149 (16%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [6,607, 8,938]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 98275
Economic Impact: $9.6 billion
Quality-Adjusted Life Years Lost: 67735

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Spain
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 20,959
• Observed Deaths: 28,732
• Excess Deaths: 7,773
• Excess Mortality Rate: 37.1%
• P-score: 37.1%
• Z-score: 5.96 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -3.8% (777 deaths)
• 45-64 years: 12.7% (1,943 deaths)
• 65-74 years: 27.0% (1,943 deaths)
• 75+ years: 20.1% (3,109 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 6,116 (58%)
• Indirect (probable): 1,897 (23%)
• Collateral (delayed care): 1,149 (16%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [6,607, 8,938]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 98275
Economic Impact: $9.6 billion
Quality-Adjusted Life Years Lost: 67735


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2023

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2021
• Experience Adjustment: 107%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.01
• Credibility Factor: 0.92
• Indicated Change: -2.4%

FINANCIAL IMPACT:
• Reserve Change: $6.1 million
• Funded Ratio Impact: -0.5%

Recommendation: Update assumptions

Human: Perform mortality assumption review for pension plan

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2023

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2021
• Experience Adjustment: 107%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.01
• Credibility Factor: 0.92
• Indicated Change: -2.4%

FINANCIAL IMPACT:
• Reserve Change: $6.1 million
• Funded Ratio Impact: -0.5%

Recommendation: Update assumptions


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 349.6
• $25-50k: 1077.3
• $50-75k: 1031.0
• $75-100k: 588.9
• >$100k: 406.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.38
• Rate Difference: 558.1 per 100,000
• Population Attributable Risk: 18.3%
• Gini Coefficient: 0.304

LIFE EXPECTANCY BY INCOME:
• <$25k: 75.8 years
• $25-50k: 75.4 years
• $50-75k: 83.1 years
• $75-100k: 73.1 years
• >$100k: 77.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 22% of disparity
• Socioeconomic Status: 15% of disparity
• Environmental Factors: 20% of disparity
• Behavioral Factors: 14% of disparity
• Biological Factors: 7% of disparity

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

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: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 349.6
• $25-50k: 1077.3
• $50-75k: 1031.0
• $75-100k: 588.9
• >$100k: 406.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.38
• Rate Difference: 558.1 per 100,000
• Population Attributable Risk: 18.3%
• Gini Coefficient: 0.304

LIFE EXPECTANCY BY INCOME:
• <$25k: 75.8 years
• $25-50k: 75.4 years
• $50-75k: 83.1 years
• $75-100k: 73.1 years
• >$100k: 77.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 22% of disparity
• Socioeconomic Status: 15% of disparity
• Environmental Factors: 20% of disparity
• Behavioral Factors: 14% of disparity
• Biological Factors: 7% of disparity

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

Social determinants explain 70% of observed mortality differences.


Instruction: Calculate policy reserve for 39 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: 29
• Current Age: 39
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1434.97
• Present Value Future Benefits (PVFB): $45038.48
• Present Value Future Premiums (PVFP): $24424.27

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $18654.99
• Per $1,000 Face: $186.55

PROSPECTIVE METHOD:
• A₁_39:10⌉ = 0.1827
• ä_39:10⌉ = 9.1693
• ₁₀V = 100,000 × A₁ - P × ä = $18654.99

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11060.76
• Accumulated Cost of Insurance: $3604.05
• Interest Earned: $1207.14
• ₁₀V = $18654.99

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $17722.24
• Tax Reserve: $17162.59
• GAAP Reserve: $19587.74

Human: Calculate policy reserve for 39 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: 29
• Current Age: 39
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1434.97
• Present Value Future Benefits (PVFB): $45038.48
• Present Value Future Premiums (PVFP): $24424.27

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $18654.99
• Per $1,000 Face: $186.55

PROSPECTIVE METHOD:
• A₁_39:10⌉ = 0.1827
• ä_39:10⌉ = 9.1693
• ₁₀V = 100,000 × A₁ - P × ä = $18654.99

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11060.76
• Accumulated Cost of Insurance: $3604.05
• Interest Earned: $1207.14
• ₁₀V = $18654.99

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $17722.24
• Tax Reserve: $17162.59
• GAAP Reserve: $19587.74