Definition
Force of mortality is the continuous-time formulation of the hazard rate for death at a specified age — the instantaneous rate at which death is occurring among those still alive at that age, expressed as a rate per unit of time.
Why it matters
Force of mortality is the version of the hazard rate used in actuarial mathematics and demographic models, including the Gompertz functional form. The continuous-time formulation is what allows mortality assumptions to be applied to arrangements with arbitrary deferral periods, payout structures, and survivorship features.
How it works
Force of mortality and hazard rate describe the same underlying concept; force of mortality is the term used when the rate is treated as a continuous function of age. By construction, the force of mortality at a given age is the instantaneous rate of dying among those who have survived to that age. Integrating the force of mortality across an age interval determines the probability of surviving across that interval — which is how survival curves are typically constructed in actuarial mathematics. Concrete figures for a US female: the force of mortality is roughly 1% per year at age 67, roughly 3% at 77, roughly 7% at 85, and roughly 18% at 95. The continuous-time form is preferred in actuarial pricing because it admits closed-form survival probability calculations under standard functional families such as the Gompertz form.
In practice
Most individuals will not encounter force of mortality by name, but the mortality assumptions in any annuity quote, life insurance premium, or pension valuation they receive are typically expressed in this form internally. The continuous-time formulation is what allows actuarial pricing to be computed under arbitrary deferral periods and payout structures — deferred annuities and survivorship products in particular rely on it. The professional pricing such products is working with the force of mortality directly; the participant experiences the effect through quoted income rates, deferral multipliers, and survivorship discounts. The practical takeaway is that the steep rise of the force of mortality with age is the structural reason that deferred income arrangements concentrate mortality credits onto a smaller surviving cohort.
In the Longevity Standard Framework
Force of mortality is the structural mechanism underlying the continuous-time mortality calculations in the Longevity Standard framework. The framework's actuarial engine uses the Gompertz form of force of mortality with female focal parameters (m=89, b=10), scaled by Society of Actuaries credibility tables, to compute the survival probabilities used in solo drawdown, the frictionless pool benchmark, and the SPIA and DIA product benchmarks. The deferral multiplier — the factor by which DIA arrangements produce more income per premium dollar than immediate alternatives — is a direct consequence of the force of mortality rising with age across the deferral period.
Related terms
- Hazard rate
- Gompertz law
- Survival curve
- Mortality rate
- Mortality table
- Deferral multiplier
- Mortality credits
- Life expectancy