Instruction: Calculate Variable Universal Life life insurance premium for 64 year old female, $500,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 64
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_64): 0.003685
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 80% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2763.41
• Expense Charge: $690.85
• Reserve Accumulation: $921.14
• Profit Margin: $230.28
• Gross Annual Premium: $4605.68

PAYMENT OPTIONS:
• Annual: $4605.68
• Semi-Annual: $2394.96 (x2 = $4789.91/year)
• Quarterly: $1220.51 (x4 = $4882.03/year)
• Monthly: $414.51 (x12 = $4974.14/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3454.26
• First Year Reserve: $921.14
• Terminal Reserve (Year 1): $305955.22

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

Internal Rate of Return: 8.6%
Profit Margin: 14.1%
Lapse Assumption: 7.7% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 64 year old female, $500,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 64
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_64): 0.003685
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 80% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2763.41
• Expense Charge: $690.85
• Reserve Accumulation: $921.14
• Profit Margin: $230.28
• Gross Annual Premium: $4605.68

PAYMENT OPTIONS:
• Annual: $4605.68
• Semi-Annual: $2394.96 (x2 = $4789.91/year)
• Quarterly: $1220.51 (x4 = $4882.03/year)
• Monthly: $414.51 (x12 = $4974.14/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3454.26
• First Year Reserve: $921.14
• Terminal Reserve (Year 1): $305955.22

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

Internal Rate of Return: 8.6%
Profit Margin: 14.1%
Lapse Assumption: 7.7% annual

Illustration assumes guaranteed rates. Actual results may vary.


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): $913.50
• Present Value Future Benefits (PVFB): $46678.96
• Present Value Future Premiums (PVFP): $39548.93

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $21783.44
• Per $1,000 Face: $217.83

PROSPECTIVE METHOD:
• A₁_63:10⌉ = 0.2032
• ä_63:10⌉ = 8.7823
• ₁₀V = 100,000 × A₁ - P × ä = $21783.44

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8730.45
• Accumulated Cost of Insurance: $3485.01
• Interest Earned: $1461.47
• ₁₀V = $21783.44

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $20694.27
• Tax Reserve: $20040.77
• GAAP Reserve: $22872.61

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): $913.50
• Present Value Future Benefits (PVFB): $46678.96
• Present Value Future Premiums (PVFP): $39548.93

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $21783.44
• Per $1,000 Face: $217.83

PROSPECTIVE METHOD:
• A₁_63:10⌉ = 0.2032
• ä_63:10⌉ = 8.7823
• ₁₀V = 100,000 × A₁ - P × ä = $21783.44

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8730.45
• Accumulated Cost of Insurance: $3485.01
• Interest Earned: $1461.47
• ₁₀V = $21783.44

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $20694.27
• Tax Reserve: $20040.77
• GAAP Reserve: $22872.61


Instruction: Compare infant mortality between Italy, Germany, India and Mexico

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Italy, Germany, India, Mexico
Reference Year: 2020

COMPARATIVE STATISTICS:
• Italy: 12.3 per 1,000 live births
• Germany: 25.0 per 1,000 live births
• India: 11.0 per 1,000 live births
• Mexico: 12.9 per 1,000 live births

RANKINGS:
1. India: 11.0
2. Italy: 12.3
3. Mexico: 12.9
4. Germany: 25.0

STATISTICAL ANALYSIS:
• Range: 13.9
• Mean: 15.3
• Median: 12.6
• Standard Deviation: 5.6
• Coefficient of Variation: 36.7%

RELATIVE COMPARISONS:
• Best vs Worst: 2.27x difference
• Above Average: 1/4
• Global Ranking: Italy: #100, Germany: #145, India: #122

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 35% of variation
• Public Health Policy: 22% of variation
• Demographics: 18% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.0% annually

Human: Compare infant mortality between Italy, Germany, India and Mexico

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Italy, Germany, India, Mexico
Reference Year: 2020

COMPARATIVE STATISTICS:
• Italy: 12.3 per 1,000 live births
• Germany: 25.0 per 1,000 live births
• India: 11.0 per 1,000 live births
• Mexico: 12.9 per 1,000 live births

RANKINGS:
1. India: 11.0
2. Italy: 12.3
3. Mexico: 12.9
4. Germany: 25.0

STATISTICAL ANALYSIS:
• Range: 13.9
• Mean: 15.3
• Median: 12.6
• Standard Deviation: 5.6
• Coefficient of Variation: 36.7%

RELATIVE COMPARISONS:
• Best vs Worst: 2.27x difference
• Above Average: 1/4
• Global Ranking: Italy: #100, Germany: #145, India: #122

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 35% of variation
• Public Health Policy: 22% of variation
• Demographics: 18% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.0% annually


Instruction: Calculate policy reserve for 50 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: 40
• Current Age: 50
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1343.48
• Present Value Future Benefits (PVFB): $49921.06
• Present Value Future Premiums (PVFP): $36221.08

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $12052.54
• Per $1,000 Face: $120.53

PROSPECTIVE METHOD:
• A₁_50:10⌉ = 0.1604
• ä_50:10⌉ = 8.8550
• ₁₀V = 100,000 × A₁ - P × ä = $12052.54

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10727.80
• Accumulated Cost of Insurance: $3374.96
• Interest Earned: $1048.45
• ₁₀V = $12052.54

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $11449.91
• Tax Reserve: $11088.34
• GAAP Reserve: $12655.17

Human: Calculate policy reserve for 50 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: 40
• Current Age: 50
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1343.48
• Present Value Future Benefits (PVFB): $49921.06
• Present Value Future Premiums (PVFP): $36221.08

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $12052.54
• Per $1,000 Face: $120.53

PROSPECTIVE METHOD:
• A₁_50:10⌉ = 0.1604
• ä_50:10⌉ = 8.8550
• ₁₀V = 100,000 × A₁ - P × ä = $12052.54

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10727.80
• Accumulated Cost of Insurance: $3374.96
• Interest Earned: $1048.45
• ₁₀V = $12052.54

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $11449.91
• Tax Reserve: $11088.34
• GAAP Reserve: $12655.17


Instruction: What is the life expectancy for a 27 year old female in Italy as of 2015?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 27 years
• Sex: Female
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 27 (e_27): 63.6 years
• Expected Age at Death: 90.6 years
• Median Survival Time: 44.1 years
• Modal Age at Death: 85.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_27): 92.6%
• 10-Year Survival (₁₀p_27): 85.7%
• 20-Year Survival (₂₀p_27): 73.4%

MORTALITY METRICS:
• Force of Mortality (μ_27): 0.01547
• Probability of Death within 1 Year (q_27): 0.01535
• Hazard Rate: 0.01559

COMPARATIVE CONTEXT:
• Global Average at Age 27: 56.4 years
• Regional Rank: Top 13 globally
• Historical Trend: Improving

Based on 432,816 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.7%.

Human: What is the life expectancy for a 27 year old female in Italy as of 2015?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 27 years
• Sex: Female
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 27 (e_27): 63.6 years
• Expected Age at Death: 90.6 years
• Median Survival Time: 44.1 years
• Modal Age at Death: 85.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_27): 92.6%
• 10-Year Survival (₁₀p_27): 85.7%
• 20-Year Survival (₂₀p_27): 73.4%

MORTALITY METRICS:
• Force of Mortality (μ_27): 0.01547
• Probability of Death within 1 Year (q_27): 0.01535
• Hazard Rate: 0.01559

COMPARATIVE CONTEXT:
• Global Average at Age 27: 56.4 years
• Regional Rank: Top 13 globally
• Historical Trend: Improving

Based on 432,816 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.7%.


Instruction: Compare infant mortality between Russia, Mexico, Japan and UK

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Russia, Mexico, Japan, UK
Reference Year: 2020

COMPARATIVE STATISTICS:
• Russia: 7.8 per 1,000 live births
• Mexico: 16.3 per 1,000 live births
• Japan: 20.4 per 1,000 live births
• UK: 5.5 per 1,000 live births

RANKINGS:
1. UK: 5.5
2. Russia: 7.8
3. Mexico: 16.3
4. Japan: 20.4

STATISTICAL ANALYSIS:
• Range: 14.9
• Mean: 12.5
• Median: 12.0
• Standard Deviation: 6.1
• Coefficient of Variation: 48.8%

RELATIVE COMPARISONS:
• Best vs Worst: 3.72x difference
• Above Average: 2/4
• Global Ranking: Russia: #110, Mexico: #32, Japan: #102

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 32% of variation
• Public Health Policy: 14% of variation
• Demographics: 12% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Converging at 0.9% annually

Human: Compare infant mortality between Russia, Mexico, Japan and UK

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Infant Mortality
Countries: Russia, Mexico, Japan, UK
Reference Year: 2020

COMPARATIVE STATISTICS:
• Russia: 7.8 per 1,000 live births
• Mexico: 16.3 per 1,000 live births
• Japan: 20.4 per 1,000 live births
• UK: 5.5 per 1,000 live births

RANKINGS:
1. UK: 5.5
2. Russia: 7.8
3. Mexico: 16.3
4. Japan: 20.4

STATISTICAL ANALYSIS:
• Range: 14.9
• Mean: 12.5
• Median: 12.0
• Standard Deviation: 6.1
• Coefficient of Variation: 48.8%

RELATIVE COMPARISONS:
• Best vs Worst: 3.72x difference
• Above Average: 2/4
• Global Ranking: Russia: #110, Mexico: #32, Japan: #102

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 32% of variation
• Public Health Policy: 14% of variation
• Demographics: 12% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Converging at 0.9% annually


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: 238.0
• Black: 710.5
• Asian: 640.0
• Hispanic: 588.5
• Native American: 569.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.49
• Rate Difference: 359.2 per 100,000
• Population Attributable Risk: 35.3%
• Gini Coefficient: 0.183

LIFE EXPECTANCY BY RACE:
• White: 70.5 years
• Black: 83.8 years
• Asian: 81.4 years
• Hispanic: 81.5 years
• Native American: 84.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 29% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 16% of disparity
• Behavioral Factors: 18% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 71% 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: 238.0
• Black: 710.5
• Asian: 640.0
• Hispanic: 588.5
• Native American: 569.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.49
• Rate Difference: 359.2 per 100,000
• Population Attributable Risk: 35.3%
• Gini Coefficient: 0.183

LIFE EXPECTANCY BY RACE:
• White: 70.5 years
• Black: 83.8 years
• Asian: 81.4 years
• Hispanic: 81.5 years
• Native American: 84.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 29% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 16% of disparity
• Behavioral Factors: 18% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 71% of observed mortality differences.


Instruction: Calculate policy reserve for 30 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 20
• Current Age: 30
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $646.67
• Present Value Future Benefits (PVFB): $42454.46
• Present Value Future Premiums (PVFP): $25325.23

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $21877.28
• Per $1,000 Face: $218.77

PROSPECTIVE METHOD:
• A₁_30:10⌉ = 0.1577
• ä_30:10⌉ = 9.8484
• ₁₀V = 100,000 × A₁ - P × ä = $21877.28

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10949.19
• Accumulated Cost of Insurance: $3908.64
• Interest Earned: $1931.33
• ₁₀V = $21877.28

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $20783.41
• Tax Reserve: $20127.09
• GAAP Reserve: $22971.14

Human: Calculate policy reserve for 30 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 20
• Current Age: 30
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $646.67
• Present Value Future Benefits (PVFB): $42454.46
• Present Value Future Premiums (PVFP): $25325.23

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $21877.28
• Per $1,000 Face: $218.77

PROSPECTIVE METHOD:
• A₁_30:10⌉ = 0.1577
• ä_30:10⌉ = 9.8484
• ₁₀V = 100,000 × A₁ - P × ä = $21877.28

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10949.19
• Accumulated Cost of Insurance: $3908.64
• Interest Earned: $1931.33
• ₁₀V = $21877.28

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $20783.41
• Tax Reserve: $20127.09
• GAAP Reserve: $22971.14


Instruction: Calculate Universal Life life insurance premium for 49 year old female, $500,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 49
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_49): 0.002235
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 91% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1877.22
• Expense Charge: $469.31
• Reserve Accumulation: $625.74
• Profit Margin: $156.44
• Gross Annual Premium: $3128.71

PAYMENT OPTIONS:
• Annual: $3128.71
• Semi-Annual: $1626.93 (x2 = $3253.86/year)
• Quarterly: $829.11 (x4 = $3316.43/year)
• Monthly: $281.58 (x12 = $3379.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2346.53
• First Year Reserve: $625.74
• Terminal Reserve (Year 16): $223357.31

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

Internal Rate of Return: 8.9%
Profit Margin: 12.4%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 49 year old female, $500,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 49
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_49): 0.002235
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 91% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1877.22
• Expense Charge: $469.31
• Reserve Accumulation: $625.74
• Profit Margin: $156.44
• Gross Annual Premium: $3128.71

PAYMENT OPTIONS:
• Annual: $3128.71
• Semi-Annual: $1626.93 (x2 = $3253.86/year)
• Quarterly: $829.11 (x4 = $3316.43/year)
• Monthly: $281.58 (x12 = $3379.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2346.53
• First Year Reserve: $625.74
• Terminal Reserve (Year 16): $223357.31

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

Internal Rate of Return: 8.9%
Profit Margin: 12.4%
Lapse Assumption: 3.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


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

Response:
POLICY RESERVE CALCULATION

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

RESERVE COMPONENTS:
• Net Level Premium (P): $1337.22
• Present Value Future Benefits (PVFB): $54540.03
• Present Value Future Premiums (PVFP): $33475.88

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $33255.04
• Per $1,000 Face: $332.55

PROSPECTIVE METHOD:
• A₁_47:10⌉ = 0.2451
• ä_47:10⌉ = 8.7307
• ₁₀V = 100,000 × A₁ - P × ä = $33255.04

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8948.32
• Accumulated Cost of Insurance: $4977.29
• Interest Earned: $1809.30
• ₁₀V = $33255.04

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $31592.28
• Tax Reserve: $30594.63
• GAAP Reserve: $34917.79

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

Actuarial AI: POLICY RESERVE CALCULATION

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

RESERVE COMPONENTS:
• Net Level Premium (P): $1337.22
• Present Value Future Benefits (PVFB): $54540.03
• Present Value Future Premiums (PVFP): $33475.88

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $33255.04
• Per $1,000 Face: $332.55

PROSPECTIVE METHOD:
• A₁_47:10⌉ = 0.2451
• ä_47:10⌉ = 8.7307
• ₁₀V = 100,000 × A₁ - P × ä = $33255.04

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8948.32
• Accumulated Cost of Insurance: $4977.29
• Interest Earned: $1809.30
• ₁₀V = $33255.04

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $31592.28
• Tax Reserve: $30594.63
• GAAP Reserve: $34917.79


Instruction: Show survival curve for Japan population in 2021

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         78.3
    1          99,997           11         0.00011         76.3
    5          99,986           27         0.00027         79.9
   10          99,959           79         0.00079         74.2
   20          99,880          132         0.00132         58.2
   30          99,748          193         0.00193         52.9
   40          99,555          372         0.00374         37.6
   50          99,183          453         0.00457         29.0
   60          98,730          817         0.00828         16.1
   70          97,913        1,279         0.01306         14.1
   80          96,634        1,394         0.01443          4.2
   90          95,240        1,944         0.02041          1.1
  100          93,296        2,976         0.03190          2.5
  110          90,320       90,320         1.00000          4.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.82

The survival curve follows Gompertz law after age 30.
Data sourced from 217,990 death certificates.

Human: Show survival curve for Japan population in 2021

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         78.3
    1          99,997           11         0.00011         76.3
    5          99,986           27         0.00027         79.9
   10          99,959           79         0.00079         74.2
   20          99,880          132         0.00132         58.2
   30          99,748          193         0.00193         52.9
   40          99,555          372         0.00374         37.6
   50          99,183          453         0.00457         29.0
   60          98,730          817         0.00828         16.1
   70          97,913        1,279         0.01306         14.1
   80          96,634        1,394         0.01443          4.2
   90          95,240        1,944         0.02041          1.1
  100          93,296        2,976         0.03190          2.5
  110          90,320       90,320         1.00000          4.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.82

The survival curve follows Gompertz law after age 30.
Data sourced from 217,990 death certificates.


Instruction: Show survival curve for Japan male in 2023

Response:
SURVIVAL CURVE ANALYSIS

Population: Japan Male
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.4
    1          99,997           16         0.00016         80.6
    5          99,981           28         0.00028         72.3
   10          99,953           74         0.00074         70.2
   20          99,879          156         0.00156         62.4
   30          99,723          219         0.00220         50.3
   40          99,504          343         0.00345         40.2
   50          99,161          571         0.00576         31.8
   60          98,590          782         0.00793         20.0
   70          97,808        1,171         0.01197         14.9
   80          96,637        2,222         0.02299          0.0
   90          94,415        2,571         0.02723          4.5
  100          91,844        4,456         0.04852          3.5
  110          87,388       87,388         1.00000          1.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.70

The survival curve follows Gompertz law after age 30.
Data sourced from 124,532 death certificates.

Human: Show survival curve for Japan male in 2023

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Japan Male
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.4
    1          99,997           16         0.00016         80.6
    5          99,981           28         0.00028         72.3
   10          99,953           74         0.00074         70.2
   20          99,879          156         0.00156         62.4
   30          99,723          219         0.00220         50.3
   40          99,504          343         0.00345         40.2
   50          99,161          571         0.00576         31.8
   60          98,590          782         0.00793         20.0
   70          97,808        1,171         0.01197         14.9
   80          96,637        2,222         0.02299          0.0
   90          94,415        2,571         0.02723          4.5
  100          91,844        4,456         0.04852          3.5
  110          87,388       87,388         1.00000          1.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.70

The survival curve follows Gompertz law after age 30.
Data sourced from 124,532 death certificates.


Instruction: Analyze mortality trends in Canada from 2004-2021

Response:
MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2004-2021

OVERALL TRENDS:
• Average Annual Change: +1.9%
• Total Change: -22.5%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.6 years.
Age-standardized death rate changed by -54 per 100,000.

KEY DRIVERS:
• Medical advances: 28% of improvement
• Public health measures: 21%
• Lifestyle changes: +23%
• Environmental factors: -8%

Human: Analyze mortality trends in Canada from 2004-2021

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2004-2021

OVERALL TRENDS:
• Average Annual Change: +1.9%
• Total Change: -22.5%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.6 years.
Age-standardized death rate changed by -54 per 100,000.

KEY DRIVERS:
• Medical advances: 28% of improvement
• Public health measures: 21%
• Lifestyle changes: +23%
• Environmental factors: -8%


Instruction: Calculate Term life insurance premium for 20 year old male, $1,000,000 coverage, 25 year term, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $1,000,000
• Term Length: 25 years
• Issue Age: 20
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.001725
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 69% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1035.00
• Expense Charge: $258.75
• Reserve Accumulation: $345.00
• Profit Margin: $86.25
• Gross Annual Premium: $1725.00

PAYMENT OPTIONS:
• Annual: $1725.00
• Semi-Annual: $897.00 (x2 = $1794.00/year)
• Quarterly: $457.12 (x4 = $1828.50/year)
• Monthly: $155.25 (x12 = $1863.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1293.75
• First Year Reserve: $345.00
• Terminal Reserve (Year 25): $394220.00

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

Internal Rate of Return: 10.0%
Profit Margin: 10.4%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 20 year old male, $1,000,000 coverage, 25 year term, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $1,000,000
• Term Length: 25 years
• Issue Age: 20
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.001725
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 69% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1035.00
• Expense Charge: $258.75
• Reserve Accumulation: $345.00
• Profit Margin: $86.25
• Gross Annual Premium: $1725.00

PAYMENT OPTIONS:
• Annual: $1725.00
• Semi-Annual: $897.00 (x2 = $1794.00/year)
• Quarterly: $457.12 (x4 = $1828.50/year)
• Monthly: $155.25 (x12 = $1863.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1293.75
• First Year Reserve: $345.00
• Terminal Reserve (Year 25): $394220.00

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

Internal Rate of Return: 10.0%
Profit Margin: 10.4%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Whole Life life insurance premium for 64 year old male, $2,000,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 64
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_64): 0.003739
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $15702.67
• Expense Charge: $3925.67
• Reserve Accumulation: $5234.22
• Profit Margin: $1308.56
• Gross Annual Premium: $26171.12

PAYMENT OPTIONS:
• Annual: $26171.12
• Semi-Annual: $13608.98 (x2 = $27217.97/year)
• Quarterly: $6935.35 (x4 = $27741.39/year)
• Monthly: $2355.40 (x12 = $28264.81/year)

RESERVE CALCULATIONS:
• Net Level Premium: $19628.34
• First Year Reserve: $5234.22
• Terminal Reserve (Year 1): $997912.87

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

Internal Rate of Return: 10.6%
Profit Margin: 14.4%
Lapse Assumption: 7.7% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 64 year old male, $2,000,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 64
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_64): 0.003739
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $15702.67
• Expense Charge: $3925.67
• Reserve Accumulation: $5234.22
• Profit Margin: $1308.56
• Gross Annual Premium: $26171.12

PAYMENT OPTIONS:
• Annual: $26171.12
• Semi-Annual: $13608.98 (x2 = $27217.97/year)
• Quarterly: $6935.35 (x4 = $27741.39/year)
• Monthly: $2355.40 (x12 = $28264.81/year)

RESERVE CALCULATIONS:
• Net Level Premium: $19628.34
• First Year Reserve: $5234.22
• Terminal Reserve (Year 1): $997912.87

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

Internal Rate of Return: 10.6%
Profit Margin: 14.4%
Lapse Assumption: 7.7% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality patterns for 1967 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1967
Current Age: 57 years
Cohort Size at Birth: 3,434,905

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 67.7 years
• Current Life Expectancy: 77.1 years
• Survival to Current Age: 63.9%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 43.9 per 1,000
• Current Mortality Rate: 41.1 per 1,000
• Improvement Since Birth: 47%

Cohort effects explain 10% of mortality variation.

Human: Analyze mortality patterns for 1967 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1967
Current Age: 57 years
Cohort Size at Birth: 3,434,905

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 67.7 years
• Current Life Expectancy: 77.1 years
• Survival to Current Age: 63.9%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 43.9 per 1,000
• Current Mortality Rate: 41.1 per 1,000
• Improvement Since Birth: 47%

Cohort effects explain 10% of mortality variation.


Instruction: Analyze mortality differences by occupation in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Occupation
Country: USA
Analysis Period: 2021

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 264.9
• Construction: 285.2
• Office: 588.3
• Transportation: 595.4
• Service: 443.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.68
• Rate Difference: 788.0 per 100,000
• Population Attributable Risk: 27.0%
• Gini Coefficient: 0.386

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 82.5 years
• Construction: 78.6 years
• Office: 80.3 years
• Transportation: 83.5 years
• Service: 70.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 34% of disparity
• Socioeconomic Status: 25% of disparity
• Environmental Factors: 25% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 7% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -0.6%

Social determinants explain 78% of observed mortality differences.

Human: Analyze mortality differences by occupation in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Occupation
Country: USA
Analysis Period: 2021

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 264.9
• Construction: 285.2
• Office: 588.3
• Transportation: 595.4
• Service: 443.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.68
• Rate Difference: 788.0 per 100,000
• Population Attributable Risk: 27.0%
• Gini Coefficient: 0.386

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 82.5 years
• Construction: 78.6 years
• Office: 80.3 years
• Transportation: 83.5 years
• Service: 70.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 34% of disparity
• Socioeconomic Status: 25% of disparity
• Environmental Factors: 25% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 7% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -0.6%

Social determinants explain 78% of observed mortality differences.


Instruction: What is the life expectancy for a 99 year old male in Canada as of 2016?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 99 years
• Sex: Male
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 99 (e_99): -2.5 years
• Expected Age at Death: 96.5 years
• Median Survival Time: -1.7 years
• Modal Age at Death: 91.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_99): 100.0%
• 10-Year Survival (₁₀p_99): 100.0%
• 20-Year Survival (₂₀p_99): 100.0%

MORTALITY METRICS:
• Force of Mortality (μ_99): -0.67440
• Probability of Death within 1 Year (q_99): -0.96286
• Hazard Rate: -0.51546

COMPARATIVE CONTEXT:
• Global Average at Age 99: -16.9 years
• Regional Rank: Top 29 globally
• Historical Trend: Improving

Based on 160,021 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.3%.

Human: What is the life expectancy for a 99 year old male in Canada as of 2016?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 99 years
• Sex: Male
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 99 (e_99): -2.5 years
• Expected Age at Death: 96.5 years
• Median Survival Time: -1.7 years
• Modal Age at Death: 91.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_99): 100.0%
• 10-Year Survival (₁₀p_99): 100.0%
• 20-Year Survival (₂₀p_99): 100.0%

MORTALITY METRICS:
• Force of Mortality (μ_99): -0.67440
• Probability of Death within 1 Year (q_99): -0.96286
• Hazard Rate: -0.51546

COMPARATIVE CONTEXT:
• Global Average at Age 99: -16.9 years
• Regional Rank: Top 29 globally
• Historical Trend: Improving

Based on 160,021 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.3%.


Instruction: Calculate policy reserve for 58 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 48
• Current Age: 58
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $882.03
• Present Value Future Benefits (PVFB): $56414.03
• Present Value Future Premiums (PVFP): $31380.40

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $31876.49
• Per $1,000 Face: $318.76

PROSPECTIVE METHOD:
• A₁_58:10⌉ = 0.2253
• ä_58:10⌉ = 9.3801
• ₁₀V = 100,000 × A₁ - P × ä = $31876.49

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8346.51
• Accumulated Cost of Insurance: $5771.65
• Interest Earned: $1880.74
• ₁₀V = $31876.49

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $30282.66
• Tax Reserve: $29326.37
• GAAP Reserve: $33470.31

Human: Calculate policy reserve for 58 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 48
• Current Age: 58
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $882.03
• Present Value Future Benefits (PVFB): $56414.03
• Present Value Future Premiums (PVFP): $31380.40

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $31876.49
• Per $1,000 Face: $318.76

PROSPECTIVE METHOD:
• A₁_58:10⌉ = 0.2253
• ä_58:10⌉ = 9.3801
• ₁₀V = 100,000 × A₁ - P × ä = $31876.49

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8346.51
• Accumulated Cost of Insurance: $5771.65
• Interest Earned: $1880.74
• ₁₀V = $31876.49

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $30282.66
• Tax Reserve: $29326.37
• GAAP Reserve: $33470.31


Instruction: Project mortality rates for Germany in 2032

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 681.2 per 100,000
• Life Expectancy: 83.4 years
• Annual Improvement: 1.10%

CONFIDENCE INTERVALS (95%):
• Lower: 579.1
• Upper: 783.4

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

Human: Project mortality rates for Germany in 2032

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 681.2 per 100,000
• Life Expectancy: 83.4 years
• Annual Improvement: 1.10%

CONFIDENCE INTERVALS (95%):
• Lower: 579.1
• Upper: 783.4

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


Instruction: Compare suburban vs other area mortality rates in USA

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 780.1
• Rural: 1006.7
• Suburban: 757.7

Rural areas show 29.0% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare suburban vs other area mortality rates in USA

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 780.1
• Rural: 1006.7
• Suburban: 757.7

Rural areas show 29.0% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Calculate Term life insurance premium for 40 year old female, $2,000,000 coverage, 15 year term, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $2,000,000
• Term Length: 15 years
• Issue Age: 40
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_40): 0.001242
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 68% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1490.02
• Expense Charge: $372.50
• Reserve Accumulation: $496.67
• Profit Margin: $124.17
• Gross Annual Premium: $2483.36

PAYMENT OPTIONS:
• Annual: $2483.36
• Semi-Annual: $1291.35 (x2 = $2582.70/year)
• Quarterly: $658.09 (x4 = $2632.36/year)
• Monthly: $223.50 (x12 = $2682.03/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1862.52
• First Year Reserve: $496.67
• Terminal Reserve (Year 15): $803683.04

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: 11.2%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 40 year old female, $2,000,000 coverage, 15 year term, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $2,000,000
• Term Length: 15 years
• Issue Age: 40
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_40): 0.001242
• Underwriting Multiplier: 0.75x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 68% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1490.02
• Expense Charge: $372.50
• Reserve Accumulation: $496.67
• Profit Margin: $124.17
• Gross Annual Premium: $2483.36

PAYMENT OPTIONS:
• Annual: $2483.36
• Semi-Annual: $1291.35 (x2 = $2582.70/year)
• Quarterly: $658.09 (x4 = $2632.36/year)
• Monthly: $223.50 (x12 = $2682.03/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1862.52
• First Year Reserve: $496.67
• Terminal Reserve (Year 15): $803683.04

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: 11.2%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate excess mortality during 2021 cold snap in France for Q1 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: France
Period: Q1 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 74,403
• Observed Deaths: 102,563
• Excess Deaths: 28,160
• Excess Mortality Rate: 37.8%
• P-score: 37.8%
• Z-score: 3.14 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 0.6% (2,816 deaths)
• 45-64 years: 18.5% (7,040 deaths)
• 65-74 years: 28.8% (7,040 deaths)
• 75+ years: 17.7% (11,264 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 15,691 (67%)
• Indirect (probable): 3,901 (19%)
• Collateral (delayed care): 2,933 (10%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [23,936, 32,383]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 348791
Economic Impact: $7.3 billion
Quality-Adjusted Life Years Lost: 306285

Human: Calculate excess mortality during 2021 cold snap in France for Q1 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: France
Period: Q1 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 74,403
• Observed Deaths: 102,563
• Excess Deaths: 28,160
• Excess Mortality Rate: 37.8%
• P-score: 37.8%
• Z-score: 3.14 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 0.6% (2,816 deaths)
• 45-64 years: 18.5% (7,040 deaths)
• 65-74 years: 28.8% (7,040 deaths)
• 75+ years: 17.7% (11,264 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 15,691 (67%)
• Indirect (probable): 3,901 (19%)
• Collateral (delayed care): 2,933 (10%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [23,936, 32,383]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 348791
Economic Impact: $7.3 billion
Quality-Adjusted Life Years Lost: 306285


Instruction: What is the life expectancy for a 51 year old male in Canada as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 51 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 51 (e_51): 25.9 years
• Expected Age at Death: 76.9 years
• Median Survival Time: 17.9 years
• Modal Age at Death: 71.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_51): 83.0%
• 10-Year Survival (₁₀p_51): 68.9%
• 20-Year Survival (₂₀p_51): 47.5%

MORTALITY METRICS:
• Force of Mortality (μ_51): 0.03719
• Probability of Death within 1 Year (q_51): 0.03650
• Hazard Rate: 0.03789

COMPARATIVE CONTEXT:
• Global Average at Age 51: 31.1 years
• Regional Rank: Top 34 globally
• Historical Trend: Stable

Based on 166,139 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.9%.

Human: What is the life expectancy for a 51 year old male in Canada as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 51 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 51 (e_51): 25.9 years
• Expected Age at Death: 76.9 years
• Median Survival Time: 17.9 years
• Modal Age at Death: 71.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_51): 83.0%
• 10-Year Survival (₁₀p_51): 68.9%
• 20-Year Survival (₂₀p_51): 47.5%

MORTALITY METRICS:
• Force of Mortality (μ_51): 0.03719
• Probability of Death within 1 Year (q_51): 0.03650
• Hazard Rate: 0.03789

COMPARATIVE CONTEXT:
• Global Average at Age 51: 31.1 years
• Regional Rank: Top 34 globally
• Historical Trend: Stable

Based on 166,139 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.9%.


Instruction: What is the life expectancy for a 6 year old both in Canada as of 2020?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 6 years
• Sex: Both
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 6 (e_6): 77.9 years
• Expected Age at Death: 83.9 years
• Median Survival Time: 54.0 years
• Modal Age at Death: 78.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_6): 93.9%
• 10-Year Survival (₁₀p_6): 88.1%
• 20-Year Survival (₂₀p_6): 77.6%

MORTALITY METRICS:
• Force of Mortality (μ_6): 0.01267
• Probability of Death within 1 Year (q_6): 0.01259
• Hazard Rate: 0.01275

COMPARATIVE CONTEXT:
• Global Average at Age 6: 76.1 years
• Regional Rank: Top 28 globally
• Historical Trend: Improving

Based on 253,940 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.

Human: What is the life expectancy for a 6 year old both in Canada as of 2020?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 6 years
• Sex: Both
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 6 (e_6): 77.9 years
• Expected Age at Death: 83.9 years
• Median Survival Time: 54.0 years
• Modal Age at Death: 78.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_6): 93.9%
• 10-Year Survival (₁₀p_6): 88.1%
• 20-Year Survival (₂₀p_6): 77.6%

MORTALITY METRICS:
• Force of Mortality (μ_6): 0.01267
• Probability of Death within 1 Year (q_6): 0.01259
• Hazard Rate: 0.01275

COMPARATIVE CONTEXT:
• Global Average at Age 6: 76.1 years
• Regional Rank: Top 28 globally
• Historical Trend: Improving

Based on 253,940 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.


Instruction: Show survival curve for Japan population in 2024

Response:
SURVIVAL CURVE ANALYSIS

Population: Japan Combined
Reference Year: 2024
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         78.8
    1          99,997           11         0.00011         77.1
    5          99,986           23         0.00023         79.7
   10          99,963           73         0.00073         66.0
   20          99,890          129         0.00129         63.0
   30          99,761          240         0.00241         54.1
   40          99,521          311         0.00312         44.4
   50          99,210          481         0.00485         30.7
   60          98,729          882         0.00893         18.2
   70          97,847        1,209         0.01236          7.1
   80          96,638        1,539         0.01593          3.2
   90          95,099        2,100         0.02208          2.3
  100          92,999        2,704         0.02908          2.4
  110          90,295       90,295         1.00000          2.0

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 76.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.6%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 167,443 death certificates.

Human: Show survival curve for Japan population in 2024

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Japan Combined
Reference Year: 2024
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         78.8
    1          99,997           11         0.00011         77.1
    5          99,986           23         0.00023         79.7
   10          99,963           73         0.00073         66.0
   20          99,890          129         0.00129         63.0
   30          99,761          240         0.00241         54.1
   40          99,521          311         0.00312         44.4
   50          99,210          481         0.00485         30.7
   60          98,729          882         0.00893         18.2
   70          97,847        1,209         0.01236          7.1
   80          96,638        1,539         0.01593          3.2
   90          95,099        2,100         0.02208          2.3
  100          92,999        2,704         0.02908          2.4
  110          90,295       90,295         1.00000          2.0

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 76.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.6%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 167,443 death certificates.


Instruction: Show survival curve for USA male in 2016

Response:
SURVIVAL CURVE ANALYSIS

Population: USA Male
Reference Year: 2016
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         80.6
    1          99,997           12         0.00012         83.9
    5          99,985           31         0.00031         78.9
   10          99,954           68         0.00068         73.2
   20          99,886          177         0.00177         60.1
   30          99,709          253         0.00254         46.8
   40          99,456          470         0.00473         38.4
   50          98,986          563         0.00569         25.2
   60          98,423        1,082         0.01099         22.9
   70          97,341        1,448         0.01488         14.4
   80          95,893        2,142         0.02234          0.0
   90          93,751        2,397         0.02557          3.8
  100          91,354        3,821         0.04183          1.8
  110          87,533       87,533         1.00000          2.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.76

The survival curve follows Gompertz law after age 30.
Data sourced from 473,608 death certificates.

Human: Show survival curve for USA male in 2016

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: USA Male
Reference Year: 2016
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         80.6
    1          99,997           12         0.00012         83.9
    5          99,985           31         0.00031         78.9
   10          99,954           68         0.00068         73.2
   20          99,886          177         0.00177         60.1
   30          99,709          253         0.00254         46.8
   40          99,456          470         0.00473         38.4
   50          98,986          563         0.00569         25.2
   60          98,423        1,082         0.01099         22.9
   70          97,341        1,448         0.01488         14.4
   80          95,893        2,142         0.02234          0.0
   90          93,751        2,397         0.02557          3.8
  100          91,354        3,821         0.04183          1.8
  110          87,533       87,533         1.00000          2.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.76

The survival curve follows Gompertz law after age 30.
Data sourced from 473,608 death certificates.


Instruction: What is the life expectancy for a 12 year old both in UK as of 2020?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: UK
• Age: 12 years
• Sex: Both
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 12 (e_12): 70.3 years
• Expected Age at Death: 82.3 years
• Median Survival Time: 48.8 years
• Modal Age at Death: 77.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_12): 93.2%
• 10-Year Survival (₁₀p_12): 86.9%
• 20-Year Survival (₂₀p_12): 75.6%

MORTALITY METRICS:
• Force of Mortality (μ_12): 0.01402
• Probability of Death within 1 Year (q_12): 0.01392
• Hazard Rate: 0.01411

COMPARATIVE CONTEXT:
• Global Average at Age 12: 69.3 years
• Regional Rank: Top 27 globally
• Historical Trend: Improving

Based on 324,189 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.

Human: What is the life expectancy for a 12 year old both in UK as of 2020?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: UK
• Age: 12 years
• Sex: Both
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 12 (e_12): 70.3 years
• Expected Age at Death: 82.3 years
• Median Survival Time: 48.8 years
• Modal Age at Death: 77.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_12): 93.2%
• 10-Year Survival (₁₀p_12): 86.9%
• 20-Year Survival (₂₀p_12): 75.6%

MORTALITY METRICS:
• Force of Mortality (μ_12): 0.01402
• Probability of Death within 1 Year (q_12): 0.01392
• Hazard Rate: 0.01411

COMPARATIVE CONTEXT:
• Global Average at Age 12: 69.3 years
• Regional Rank: Top 27 globally
• Historical Trend: Improving

Based on 324,189 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.


Instruction: Calculate excess mortality during COVID-19 pandemic in Italy for 2022

Response:
EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: Italy
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 57,629
• Observed Deaths: 84,153
• Excess Deaths: 26,524
• Excess Mortality Rate: 46.0%
• P-score: 46.0%
• Z-score: 3.62 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 9.4% (2,652 deaths)
• 45-64 years: 16.6% (6,631 deaths)
• 65-74 years: 20.6% (6,631 deaths)
• 75+ years: 30.5% (10,609 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 14,093 (54%)
• Indirect (probable): 5,950 (13%)
• Collateral (delayed care): 4,605 (16%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [22,545, 30,502]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 393718
Economic Impact: $1.4 billion
Quality-Adjusted Life Years Lost: 234242

Human: Calculate excess mortality during COVID-19 pandemic in Italy for 2022

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: Italy
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 57,629
• Observed Deaths: 84,153
• Excess Deaths: 26,524
• Excess Mortality Rate: 46.0%
• P-score: 46.0%
• Z-score: 3.62 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 9.4% (2,652 deaths)
• 45-64 years: 16.6% (6,631 deaths)
• 65-74 years: 20.6% (6,631 deaths)
• 75+ years: 30.5% (10,609 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 14,093 (54%)
• Indirect (probable): 5,950 (13%)
• Collateral (delayed care): 4,605 (16%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [22,545, 30,502]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 393718
Economic Impact: $1.4 billion
Quality-Adjusted Life Years Lost: 234242


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2021
• Experience Adjustment: 96%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.05
• Credibility Factor: 0.92
• Indicated Change: +5.5%

FINANCIAL IMPACT:
• Reserve Change: $9.2 million
• Funded Ratio Impact: -0.8%

Recommendation: Update assumptions

Human: Perform mortality assumption review for pension plan

Actuarial AI: MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2021
• Experience Adjustment: 96%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.05
• Credibility Factor: 0.92
• Indicated Change: +5.5%

FINANCIAL IMPACT:
• Reserve Change: $9.2 million
• Funded Ratio Impact: -0.8%

Recommendation: Update assumptions


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Healthcare
Fatal Injury Rate: 98.6 per 100,000 full-time workers
Annual Deaths: 4,582

LEADING CAUSES:
• Falls: 21%
• Struck by object: 17%
• Electrocution: 9%
• Caught-in/between: 10%

Workers' compensation death benefit: $437,642

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Healthcare
Fatal Injury Rate: 98.6 per 100,000 full-time workers
Annual Deaths: 4,582

LEADING CAUSES:
• Falls: 21%
• Struck by object: 17%
• Electrocution: 9%
• Caught-in/between: 10%

Workers' compensation death benefit: $437,642


Instruction: Compare maternal mortality between Spain, Mexico, Brazil, China and UK

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Spain, Mexico, Brazil, China, UK
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 38.0 per 100,000 live births
• Mexico: 21.6 per 100,000 live births
• Brazil: 19.1 per 100,000 live births
• China: 48.7 per 100,000 live births
• UK: 40.3 per 100,000 live births

RANKINGS:
1. Brazil: 19.1
2. Mexico: 21.6
3. Spain: 38.0
4. UK: 40.3
5. China: 48.7

STATISTICAL ANALYSIS:
• Range: 29.6
• Mean: 33.5
• Median: 38.0
• Standard Deviation: 11.4
• Coefficient of Variation: 33.9%

RELATIVE COMPARISONS:
• Best vs Worst: 2.55x difference
• Above Average: 3/5
• Global Ranking: Spain: #130, Mexico: #137, Brazil: #15

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 20% of variation
• Public Health Policy: 12% of variation
• Demographics: 16% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 0.9% annually

Human: Compare maternal mortality between Spain, Mexico, Brazil, China and UK

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Spain, Mexico, Brazil, China, UK
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 38.0 per 100,000 live births
• Mexico: 21.6 per 100,000 live births
• Brazil: 19.1 per 100,000 live births
• China: 48.7 per 100,000 live births
• UK: 40.3 per 100,000 live births

RANKINGS:
1. Brazil: 19.1
2. Mexico: 21.6
3. Spain: 38.0
4. UK: 40.3
5. China: 48.7

STATISTICAL ANALYSIS:
• Range: 29.6
• Mean: 33.5
• Median: 38.0
• Standard Deviation: 11.4
• Coefficient of Variation: 33.9%

RELATIVE COMPARISONS:
• Best vs Worst: 2.55x difference
• Above Average: 3/5
• Global Ranking: Spain: #130, Mexico: #137, Brazil: #15

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 20% of variation
• Public Health Policy: 12% of variation
• Demographics: 16% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 0.9% annually


Instruction: What are the mortality characteristics for middle age population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Middle Age (40-64 years)

MORTALITY METRICS:
• Death Rate: 9.21 per 1,000
• Leading Causes: Cancer, heart disease, accidents
• Preventable Deaths: 37%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for middle age population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Middle Age (40-64 years)

MORTALITY METRICS:
• Death Rate: 9.21 per 1,000
• Leading Causes: Cancer, heart disease, accidents
• Preventable Deaths: 37%

Life table analysis shows stable risk profile.


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Transportation
Fatal Injury Rate: 36.5 per 100,000 full-time workers
Annual Deaths: 2,284

LEADING CAUSES:
• Falls: 25%
• Struck by object: 28%
• Electrocution: 10%
• Caught-in/between: 10%

Workers' compensation death benefit: $405,646

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Transportation
Fatal Injury Rate: 36.5 per 100,000 full-time workers
Annual Deaths: 2,284

LEADING CAUSES:
• Falls: 25%
• Struck by object: 28%
• Electrocution: 10%
• Caught-in/between: 10%

Workers' compensation death benefit: $405,646


Instruction: Compare life expectancy between Canada and France

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Canada, France
Reference Year: 2022

COMPARATIVE STATISTICS:
• Canada: 70.7 years
• France: 81.2 years

RANKINGS:
1. France: 81.2
2. Canada: 70.7

STATISTICAL ANALYSIS:
• Range: 10.5
• Mean: 75.9
• Median: 75.9
• Standard Deviation: 5.3
• Coefficient of Variation: 6.9%

RELATIVE COMPARISONS:
• Best vs Worst: 0.87x difference
• Above Average: 1/2
• Global Ranking: Canada: #82, France: #22

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 33% of variation
• Public Health Policy: 12% of variation
• Demographics: 19% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Converging at 1.5% annually

Human: Compare life expectancy between Canada and France

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Canada, France
Reference Year: 2022

COMPARATIVE STATISTICS:
• Canada: 70.7 years
• France: 81.2 years

RANKINGS:
1. France: 81.2
2. Canada: 70.7

STATISTICAL ANALYSIS:
• Range: 10.5
• Mean: 75.9
• Median: 75.9
• Standard Deviation: 5.3
• Coefficient of Variation: 6.9%

RELATIVE COMPARISONS:
• Best vs Worst: 0.87x difference
• Above Average: 1/2
• Global Ranking: Canada: #82, France: #22

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 33% of variation
• Public Health Policy: 12% of variation
• Demographics: 19% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Converging at 1.5% annually


Instruction: What is the life expectancy for a 18 year old both in Japan as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 18 years
• Sex: Both
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 18 (e_18): 63.0 years
• Expected Age at Death: 81.0 years
• Median Survival Time: 43.7 years
• Modal Age at Death: 76.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_18): 92.5%
• 10-Year Survival (₁₀p_18): 85.5%
• 20-Year Survival (₂₀p_18): 73.2%

MORTALITY METRICS:
• Force of Mortality (μ_18): 0.01562
• Probability of Death within 1 Year (q_18): 0.01550
• Hazard Rate: 0.01574

COMPARATIVE CONTEXT:
• Global Average at Age 18: 66.6 years
• Regional Rank: Top 45 globally
• Historical Trend: Improving

Based on 145,883 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.1%.

Human: What is the life expectancy for a 18 year old both in Japan as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 18 years
• Sex: Both
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 18 (e_18): 63.0 years
• Expected Age at Death: 81.0 years
• Median Survival Time: 43.7 years
• Modal Age at Death: 76.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_18): 92.5%
• 10-Year Survival (₁₀p_18): 85.5%
• 20-Year Survival (₂₀p_18): 73.2%

MORTALITY METRICS:
• Force of Mortality (μ_18): 0.01562
• Probability of Death within 1 Year (q_18): 0.01550
• Hazard Rate: 0.01574

COMPARATIVE CONTEXT:
• Global Average at Age 18: 66.6 years
• Regional Rank: Top 45 globally
• Historical Trend: Improving

Based on 145,883 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.1%.


Instruction: Analyze mortality patterns for 1929 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1929
Current Age: 95 years
Cohort Size at Birth: 2,179,548

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.6 years
• Current Life Expectancy: 76.6 years
• Survival to Current Age: 77.8%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 12.0 per 1,000
• Current Mortality Rate: 5.4 per 1,000
• Improvement Since Birth: 37%

Cohort effects explain 13% of mortality variation.

Human: Analyze mortality patterns for 1929 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1929
Current Age: 95 years
Cohort Size at Birth: 2,179,548

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.6 years
• Current Life Expectancy: 76.6 years
• Survival to Current Age: 77.8%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 12.0 per 1,000
• Current Mortality Rate: 5.4 per 1,000
• Improvement Since Birth: 37%

Cohort effects explain 13% of mortality variation.


Instruction: Calculate Universal Life life insurance premium for 52 year old female, $250,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 52
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.002223
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $933.59
• Expense Charge: $233.40
• Reserve Accumulation: $311.20
• Profit Margin: $77.80
• Gross Annual Premium: $1555.99

PAYMENT OPTIONS:
• Annual: $1555.99
• Semi-Annual: $809.12 (x2 = $1618.23/year)
• Quarterly: $412.34 (x4 = $1649.35/year)
• Monthly: $140.04 (x12 = $1680.47/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1166.99
• First Year Reserve: $311.20
• Terminal Reserve (Year 13): $172313.87

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

Internal Rate of Return: 8.8%
Profit Margin: 12.1%
Lapse Assumption: 4.9% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 52 year old female, $250,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 52
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.002223
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $933.59
• Expense Charge: $233.40
• Reserve Accumulation: $311.20
• Profit Margin: $77.80
• Gross Annual Premium: $1555.99

PAYMENT OPTIONS:
• Annual: $1555.99
• Semi-Annual: $809.12 (x2 = $1618.23/year)
• Quarterly: $412.34 (x4 = $1649.35/year)
• Monthly: $140.04 (x12 = $1680.47/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1166.99
• First Year Reserve: $311.20
• Terminal Reserve (Year 13): $172313.87

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

Internal Rate of Return: 8.8%
Profit Margin: 12.1%
Lapse Assumption: 4.9% annual

Illustration assumes guaranteed rates. Actual results may vary.


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 81.5 per 100,000 full-time workers
Annual Deaths: 5,892

LEADING CAUSES:
• Falls: 38%
• Struck by object: 28%
• Electrocution: 8%
• Caught-in/between: 19%

Workers' compensation death benefit: $360,788

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 81.5 per 100,000 full-time workers
Annual Deaths: 5,892

LEADING CAUSES:
• Falls: 38%
• Struck by object: 28%
• Electrocution: 8%
• Caught-in/between: 19%

Workers' compensation death benefit: $360,788


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2022

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 624.1
• $25-50k: 999.4
• $50-75k: 633.5
• $75-100k: 489.0
• >$100k: 1030.8

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.69
• Rate Difference: 646.8 per 100,000
• Population Attributable Risk: 21.9%
• Gini Coefficient: 0.255

LIFE EXPECTANCY BY INCOME:
• <$25k: 72.3 years
• $25-50k: 81.7 years
• $50-75k: 83.3 years
• $75-100k: 76.7 years
• >$100k: 75.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 35% of disparity
• Socioeconomic Status: 34% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.1%

Social determinants explain 73% of observed mortality differences.

Human: Analyze mortality differences by income in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2022

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 624.1
• $25-50k: 999.4
• $50-75k: 633.5
• $75-100k: 489.0
• >$100k: 1030.8

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.69
• Rate Difference: 646.8 per 100,000
• Population Attributable Risk: 21.9%
• Gini Coefficient: 0.255

LIFE EXPECTANCY BY INCOME:
• <$25k: 72.3 years
• $25-50k: 81.7 years
• $50-75k: 83.3 years
• $75-100k: 76.7 years
• >$100k: 75.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 35% of disparity
• Socioeconomic Status: 34% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.1%

Social determinants explain 73% of observed mortality differences.


Instruction: Calculate policy reserve for 68 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: 58
• Current Age: 68
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1064.87
• Present Value Future Benefits (PVFB): $59157.96
• Present Value Future Premiums (PVFP): $33165.72

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $32315.21
• Per $1,000 Face: $323.15

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.1605
• ä_68:10⌉ = 8.8039
• ₁₀V = 100,000 × A₁ - P × ä = $32315.21

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8273.39
• Accumulated Cost of Insurance: $4889.26
• Interest Earned: $1588.01
• ₁₀V = $32315.21

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $30699.45
• Tax Reserve: $29729.99
• GAAP Reserve: $33930.97

Human: Calculate policy reserve for 68 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: 58
• Current Age: 68
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1064.87
• Present Value Future Benefits (PVFB): $59157.96
• Present Value Future Premiums (PVFP): $33165.72

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $32315.21
• Per $1,000 Face: $323.15

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.1605
• ä_68:10⌉ = 8.8039
• ₁₀V = 100,000 × A₁ - P × ä = $32315.21

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8273.39
• Accumulated Cost of Insurance: $4889.26
• Interest Earned: $1588.01
• ₁₀V = $32315.21

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $30699.45
• Tax Reserve: $29729.99
• GAAP Reserve: $33930.97


Instruction: Calculate Universal Life life insurance premium for 30 year old male, $100,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 30
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_30): 0.002407
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $404.45
• Expense Charge: $101.11
• Reserve Accumulation: $134.82
• Profit Margin: $33.70
• Gross Annual Premium: $674.08

PAYMENT OPTIONS:
• Annual: $674.08
• Semi-Annual: $350.52 (x2 = $701.04/year)
• Quarterly: $178.63 (x4 = $714.53/year)
• Monthly: $60.67 (x12 = $728.01/year)

RESERVE CALCULATIONS:
• Net Level Premium: $505.56
• First Year Reserve: $134.82
• Terminal Reserve (Year 35): $64718.68

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

Internal Rate of Return: 9.7%
Profit Margin: 12.7%
Lapse Assumption: 6.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 30 year old male, $100,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 30
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_30): 0.002407
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $404.45
• Expense Charge: $101.11
• Reserve Accumulation: $134.82
• Profit Margin: $33.70
• Gross Annual Premium: $674.08

PAYMENT OPTIONS:
• Annual: $674.08
• Semi-Annual: $350.52 (x2 = $701.04/year)
• Quarterly: $178.63 (x4 = $714.53/year)
• Monthly: $60.67 (x12 = $728.01/year)

RESERVE CALCULATIONS:
• Net Level Premium: $505.56
• First Year Reserve: $134.82
• Terminal Reserve (Year 35): $64718.68

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

Internal Rate of Return: 9.7%
Profit Margin: 12.7%
Lapse Assumption: 6.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare urban vs other area mortality rates in UK

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 854.9
• Rural: 994.4
• Suburban: 772.1

Rural areas show 16.3% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare urban vs other area mortality rates in UK

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 854.9
• Rural: 994.4
• Suburban: 772.1

Rural areas show 16.3% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: What is the mortality rate for Chronic Respiratory in France for Under 25 in 2024?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: France
Year: 2024
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 37.1 per 100,000 population
• Age-Adjusted Rate: 33.7 per 100,000
• Total Deaths: 123,123
• Percentage of All Deaths: 13.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 44.5 per 100,000
• Female Death Rate: 31.5 per 100,000
• Sex Ratio (M:F): 1.29:1

TREND ANALYSIS:
• 5-Year Change: -8.7%
• 10-Year Change: -17.9%
• Annual Percentage Change: +1.0%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 2677688
• Economic Burden: $97.0 billion annually
• Preventable Deaths: 49%

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

International Classification of Diseases (ICD-10): J40-J47
Data Quality: Partial (92% coverage)

Human: What is the mortality rate for Chronic Respiratory in France for Under 25 in 2024?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: France
Year: 2024
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 37.1 per 100,000 population
• Age-Adjusted Rate: 33.7 per 100,000
• Total Deaths: 123,123
• Percentage of All Deaths: 13.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 44.5 per 100,000
• Female Death Rate: 31.5 per 100,000
• Sex Ratio (M:F): 1.29:1

TREND ANALYSIS:
• 5-Year Change: -8.7%
• 10-Year Change: -17.9%
• Annual Percentage Change: +1.0%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 2677688
• Economic Burden: $97.0 billion annually
• Preventable Deaths: 49%

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

International Classification of Diseases (ICD-10): J40-J47
Data Quality: Partial (92% coverage)


Instruction: Project mortality rates for UK in 2030

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 805.8 per 100,000
• Life Expectancy: 83.7 years
• Annual Improvement: 1.75%

CONFIDENCE INTERVALS (95%):
• Lower: 685.0
• Upper: 926.7

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

Human: Project mortality rates for UK in 2030

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 805.8 per 100,000
• Life Expectancy: 83.7 years
• Annual Improvement: 1.75%

CONFIDENCE INTERVALS (95%):
• Lower: 685.0
• Upper: 926.7

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


Instruction: Show survival curve for China female in 2015

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         83.9
    1          99,998            9         0.00009         77.9
    5          99,989           21         0.00021         70.7
   10          99,968           61         0.00061         69.2
   20          99,907          118         0.00118         57.7
   30          99,789          162         0.00162         48.1
   40          99,627          249         0.00250         36.5
   50          99,378          471         0.00474         31.8
   60          98,907          640         0.00647         21.2
   70          98,267        1,103         0.01122         12.7
   80          97,164        1,526         0.01571          0.0
   90          95,638        1,948         0.02037          3.1
  100          93,690        2,226         0.02376          3.4
  110          91,464       91,464         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.2%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 323,341 death certificates.

Human: Show survival curve for China female in 2015

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         83.9
    1          99,998            9         0.00009         77.9
    5          99,989           21         0.00021         70.7
   10          99,968           61         0.00061         69.2
   20          99,907          118         0.00118         57.7
   30          99,789          162         0.00162         48.1
   40          99,627          249         0.00250         36.5
   50          99,378          471         0.00474         31.8
   60          98,907          640         0.00647         21.2
   70          98,267        1,103         0.01122         12.7
   80          97,164        1,526         0.01571          0.0
   90          95,638        1,948         0.02037          3.1
  100          93,690        2,226         0.02376          3.4
  110          91,464       91,464         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.2%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 323,341 death certificates.


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

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

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

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 55 (e_55): 28.9 years
• Expected Age at Death: 83.9 years
• Median Survival Time: 20.0 years
• Modal Age at Death: 78.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_55): 84.6%
• 10-Year Survival (₁₀p_55): 71.6%
• 20-Year Survival (₂₀p_55): 51.2%

MORTALITY METRICS:
• Force of Mortality (μ_55): 0.03345
• Probability of Death within 1 Year (q_55): 0.03290
• Hazard Rate: 0.03402

COMPARATIVE CONTEXT:
• Global Average at Age 55: 29.6 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 471,795 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.2%.

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

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

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

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 55 (e_55): 28.9 years
• Expected Age at Death: 83.9 years
• Median Survival Time: 20.0 years
• Modal Age at Death: 78.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_55): 84.6%
• 10-Year Survival (₁₀p_55): 71.6%
• 20-Year Survival (₂₀p_55): 51.2%

MORTALITY METRICS:
• Force of Mortality (μ_55): 0.03345
• Probability of Death within 1 Year (q_55): 0.03290
• Hazard Rate: 0.03402

COMPARATIVE CONTEXT:
• Global Average at Age 55: 29.6 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 471,795 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.2%.


Instruction: Calculate policy reserve for 46 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 36
• Current Age: 46
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1434.69
• Present Value Future Benefits (PVFB): $42368.09
• Present Value Future Premiums (PVFP): $32004.55

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $11845.08
• Per $1,000 Face: $118.45

PROSPECTIVE METHOD:
• A₁_46:10⌉ = 0.1957
• ä_46:10⌉ = 8.6290
• ₁₀V = 100,000 × A₁ - P × ä = $11845.08

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10290.27
• Accumulated Cost of Insurance: $5777.31
• Interest Earned: $1043.93
• ₁₀V = $11845.08

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $11252.82
• Tax Reserve: $10897.47
• GAAP Reserve: $12437.33

Human: Calculate policy reserve for 46 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 36
• Current Age: 46
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1434.69
• Present Value Future Benefits (PVFB): $42368.09
• Present Value Future Premiums (PVFP): $32004.55

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $11845.08
• Per $1,000 Face: $118.45

PROSPECTIVE METHOD:
• A₁_46:10⌉ = 0.1957
• ä_46:10⌉ = 8.6290
• ₁₀V = 100,000 × A₁ - P × ä = $11845.08

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10290.27
• Accumulated Cost of Insurance: $5777.31
• Interest Earned: $1043.93
• ₁₀V = $11845.08

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $11252.82
• Tax Reserve: $10897.47
• GAAP Reserve: $12437.33


Instruction: Calculate excess mortality during 2022 heat wave in Germany for Q2 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Germany
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 48,135
• Observed Deaths: 58,682
• Excess Deaths: 10,547
• Excess Mortality Rate: 21.9%
• P-score: 21.9%
• Z-score: 3.68 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 2.4% (1,054 deaths)
• 45-64 years: 16.9% (2,636 deaths)
• 65-74 years: 23.1% (2,636 deaths)
• 75+ years: 39.9% (4,218 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 7,725 (61%)
• Indirect (probable): 2,412 (20%)
• Collateral (delayed care): 1,583 (12%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,964, 12,129]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 127967
Economic Impact: $6.6 billion
Quality-Adjusted Life Years Lost: 114153

Human: Calculate excess mortality during 2022 heat wave in Germany for Q2 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Germany
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 48,135
• Observed Deaths: 58,682
• Excess Deaths: 10,547
• Excess Mortality Rate: 21.9%
• P-score: 21.9%
• Z-score: 3.68 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 2.4% (1,054 deaths)
• 45-64 years: 16.9% (2,636 deaths)
• 65-74 years: 23.1% (2,636 deaths)
• 75+ years: 39.9% (4,218 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 7,725 (61%)
• Indirect (probable): 2,412 (20%)
• Collateral (delayed care): 1,583 (12%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,964, 12,129]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 127967
Economic Impact: $6.6 billion
Quality-Adjusted Life Years Lost: 114153


Instruction: Calculate Universal Life life insurance premium for 66 year old male, $5,000,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 66
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_66): 0.003996
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 97% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $33570.41
• Expense Charge: $8392.60
• Reserve Accumulation: $11190.14
• Profit Margin: $2797.53
• Gross Annual Premium: $55950.68

PAYMENT OPTIONS:
• Annual: $55950.68
• Semi-Annual: $29094.35 (x2 = $58188.70/year)
• Quarterly: $14826.93 (x4 = $59307.72/year)
• Monthly: $5035.56 (x12 = $60426.73/year)

RESERVE CALCULATIONS:
• Net Level Premium: $41963.01
• First Year Reserve: $11190.14
• Terminal Reserve (Year -1): $2741424.56

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

Internal Rate of Return: 11.3%
Profit Margin: 11.5%
Lapse Assumption: 3.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 66 year old male, $5,000,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 66
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_66): 0.003996
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 97% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $33570.41
• Expense Charge: $8392.60
• Reserve Accumulation: $11190.14
• Profit Margin: $2797.53
• Gross Annual Premium: $55950.68

PAYMENT OPTIONS:
• Annual: $55950.68
• Semi-Annual: $29094.35 (x2 = $58188.70/year)
• Quarterly: $14826.93 (x4 = $59307.72/year)
• Monthly: $5035.56 (x12 = $60426.73/year)

RESERVE CALCULATIONS:
• Net Level Premium: $41963.01
• First Year Reserve: $11190.14
• Terminal Reserve (Year -1): $2741424.56

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

Internal Rate of Return: 11.3%
Profit Margin: 11.5%
Lapse Assumption: 3.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare cardiovascular mortality between Japan, Mexico, Brazil and Italy

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Japan, Mexico, Brazil, Italy
Reference Year: 2020

COMPARATIVE STATISTICS:
• Japan: 185.6 per 100,000 population
• Mexico: 84.9 per 100,000 population
• Brazil: 186.3 per 100,000 population
• Italy: 58.7 per 100,000 population

RANKINGS:
1. Italy: 58.7
2. Mexico: 84.9
3. Japan: 185.6
4. Brazil: 186.3

STATISTICAL ANALYSIS:
• Range: 127.6
• Mean: 128.9
• Median: 135.3
• Standard Deviation: 57.8
• Coefficient of Variation: 44.9%

RELATIVE COMPARISONS:
• Best vs Worst: 3.17x difference
• Above Average: 2/4
• Global Ranking: Japan: #8, Mexico: #44, Brazil: #139

CONTRIBUTING FACTORS:
• Healthcare System: 26% of variation
• Economic Development: 33% of variation
• Public Health Policy: 16% of variation
• Demographics: 11% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Converging at 1.6% annually

Human: Compare cardiovascular mortality between Japan, Mexico, Brazil and Italy

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Japan, Mexico, Brazil, Italy
Reference Year: 2020

COMPARATIVE STATISTICS:
• Japan: 185.6 per 100,000 population
• Mexico: 84.9 per 100,000 population
• Brazil: 186.3 per 100,000 population
• Italy: 58.7 per 100,000 population

RANKINGS:
1. Italy: 58.7
2. Mexico: 84.9
3. Japan: 185.6
4. Brazil: 186.3

STATISTICAL ANALYSIS:
• Range: 127.6
• Mean: 128.9
• Median: 135.3
• Standard Deviation: 57.8
• Coefficient of Variation: 44.9%

RELATIVE COMPARISONS:
• Best vs Worst: 3.17x difference
• Above Average: 2/4
• Global Ranking: Japan: #8, Mexico: #44, Brazil: #139

CONTRIBUTING FACTORS:
• Healthcare System: 26% of variation
• Economic Development: 33% of variation
• Public Health Policy: 16% of variation
• Demographics: 11% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Converging at 1.6% annually


Instruction: Compare life expectancy between Spain, Italy, South Korea and China

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Spain, Italy, South Korea, China
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 72.2 years
• Italy: 73.6 years
• South Korea: 70.4 years
• China: 78.6 years

RANKINGS:
1. China: 78.6
2. Italy: 73.6
3. Spain: 72.2
4. South Korea: 70.4

STATISTICAL ANALYSIS:
• Range: 8.2
• Mean: 73.7
• Median: 72.9
• Standard Deviation: 3.1
• Coefficient of Variation: 4.1%

RELATIVE COMPARISONS:
• Best vs Worst: 0.90x difference
• Above Average: 1/4
• Global Ranking: Spain: #131, Italy: #43, South Korea: #64

CONTRIBUTING FACTORS:
• Healthcare System: 35% of variation
• Economic Development: 17% of variation
• Public Health Policy: 21% of variation
• Demographics: 15% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Converging at 1.2% annually

Human: Compare life expectancy between Spain, Italy, South Korea and China

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Spain, Italy, South Korea, China
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 72.2 years
• Italy: 73.6 years
• South Korea: 70.4 years
• China: 78.6 years

RANKINGS:
1. China: 78.6
2. Italy: 73.6
3. Spain: 72.2
4. South Korea: 70.4

STATISTICAL ANALYSIS:
• Range: 8.2
• Mean: 73.7
• Median: 72.9
• Standard Deviation: 3.1
• Coefficient of Variation: 4.1%

RELATIVE COMPARISONS:
• Best vs Worst: 0.90x difference
• Above Average: 1/4
• Global Ranking: Spain: #131, Italy: #43, South Korea: #64

CONTRIBUTING FACTORS:
• Healthcare System: 35% of variation
• Economic Development: 17% of variation
• Public Health Policy: 21% of variation
• Demographics: 15% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Converging at 1.2% annually