Definition
Gompertz law is the empirical regularity, first identified by Benjamin Gompertz in 1825, that adult mortality rates rise approximately exponentially with age across much of the adult lifespan, providing a compact functional form for representing age-specific mortality.
Why it matters
Gompertz law is the simplest functional form that fits adult human mortality reasonably well across most of the lifespan, and it is therefore the workhorse model in actuarial science, demography, and biological aging research. Many lifetime income calculations — including those in the Longevity Standard framework's actuarial engine — use a Gompertz-form mortality curve as their structural primitive.
How it works
The Gompertz form represents the force of mortality as growing geometrically with age — doubling roughly every seven to ten years across much of the adult range. The functional form has two parameters: a level parameter often expressed as a modal age at death (the age at which the cohort's mortality density peaks) and a slope parameter often expressed as a doubling-time scale (governing how rapidly mortality rises with age). The two parameters together fit observed adult mortality with remarkable economy. Concrete figures using a focal female parameterization (modal age in the high 80s, doubling-time scale around a decade): the force of mortality is roughly 1% per year at age 67, doubling to roughly 3% by age 77, to roughly 7% by 85, and to roughly 18% by 95. The fit holds well between roughly age 30 and age 95; at the extreme ages (above 100), observed mortality typically rises less steeply than Gompertz predicts, which is why extensions of the form (Gompertz-Makeham, logistic) are used to capture the late-life plateau.
In practice
Most individuals do not encounter Gompertz law directly but rely on its outputs every time they receive an annuity quote, a life insurance premium, or a long-horizon retirement projection. The practical implication of the law is that mortality risk grows geometrically with age — which is the structural reason that the value of pooled and deferred lifetime income arrangements rises sharply with planning horizon and with starting age. A professional working with mortality models is generally working with Gompertz or a Gompertz-extended form. Individuals comparing arrangements at different starting ages should expect the relative value of pooling and deferral to shift substantially with the starting age, because the underlying Gompertz growth is fast.
In the Longevity Standard Framework
Gompertz law is the structural mechanism underlying the mortality assumption in the Longevity Standard actuarial engine. The engine's canonical focal individual configuration uses Gompertz with female parameters m=89/b=10, scaled by Society of Actuaries credibility tables; the same parameterization drives the survival probabilities used in the solo drawdown baseline, the frictionless pool benchmark, and the SPIA and DIA product benchmarks. The locked numerical findings in the framework — solo drawdown income, frictionless pooled income, SPIA and DIA benchmarks, pooling multiplier, deferral multiplier — all derive from this Gompertz-form mortality assumption at the focal-individual parameters.
Related terms
- Force of mortality
- Hazard rate
- Mortality rate
- Survival curve
- Mortality table
- Mortality improvement
- Cohort effect
- Longevity risk