Actuarial Applications
Mathematical tools for actuarial science — mortality modelling, non-life loss reserving, life insurance pricing, pension valuations, and credibility theory. Built on internationally recognised standards (SOA, CAS, IFoA). Use the Loss Reserving tab to run an interactive Chain-Ladder model on your own triangle data.
Standard Mortality Table (Illustrative)
Live Demo| Age x | lₓ | dₓ | qₓ | eₓ |
|---|---|---|---|---|
| 30 | 100,000 | 152 | 0.001520 | 49.27 |
| 35 | 99,541 | 220 | 0.002210 | 44.39 |
| 40 | 98,742 | 346 | 0.003504 | 39.64 |
| 45 | 97,536 | 560 | 0.005742 | 34.97 |
| 50 | 95,813 | 891 | 0.009299 | 30.44 |
| 55 | 93,421 | 1,390 | 0.014881 | 26.12 |
| 60 | 89,842 | 2,121 | 0.023607 | 21.98 |
| 65 | 83,718 | 3,210 | 0.038340 | 18.09 |
| 70 | 73,841 | 4,812 | 0.065167 | 14.45 |
| 75 | 59,327 | 6,901 | 0.116323 | 11.14 |
Illustrative life table — lₓ = lives, dₓ = deaths, qₓ = mortality rate, eₓ = curtate expectation of life
Survival Function S(x)
Live DemoS(x) = P(T > x) — probability of surviving beyond age x
Key Definitions
Live DemoForce of mortality (μₓ)−d/dx ln S(x)
Complete life expectancy (ė)∫₀^ω S(x) dx
Curtate life expectancy (e)Σ ₖpₓ
Makeham's Law (μₓ)A + Bcˣ
Gompertz's Law (μₓ)Bcˣ