Survival models playground
Mortality as a law instead of a table: a constant accident hazard plus an ageing term that compounds relentlessly. Slide the parameters and watch the survival curve, the force of mortality and life expectancy respond.
Survival from age 30, ₜp₍ₓ₎
Force of mortality, μ₍ₓ₎ = A + Bcˣ
Gompertz-Makeham: A is the constant accident hazard, B and c set the ageing term Bcˣ that compounds every year — mortality doubling roughly every 8 years at this c. Survival has the closed form ₜp₍ₓ₎ = exp(−At − Bcˣ(cᵗ−1)/ln c); life expectancy is the area under the curve. Parameters here are illustrative, not any published table.
Why a parametric law
Real pricing uses graduated tables, but the Gompertz-Makeham law is how the exams build intuition: A captures age-independent hazards, and the Bcˣ term captures ageing — human mortality really does double about every eight to nine years of adult life, which is why the force curve explodes on the right while the survival curve holds up and then collapses. The parameters here are illustrative only; no values from any published mortality table appear on this page.
Make it stick. Studying CS2 or CM1? Survival models lead straight into the life contingencies notation in our notation cheat sheet covers the symbols. Memori is a flashcard app built by actuarial students — join the beta.
For education only, not financial advice.