Definition
A survival curve is a graphical or tabular representation of the share of a starting cohort still alive at each successive age, declining from one at the entry age to zero at the oldest age any member reaches.
Why it matters
The survival curve is the structural visualization that makes the shape of mortality experience legible at a glance. Many findings about lifetime income — the compression of cost ranges across planning horizons, the steepness of the cost-of-extra-protection curve, the rising value of pooling at advanced ages — are direct consequences of survival-curve shape rather than abstract mathematical properties.
How it works
A survival curve at a given starting age begins at 1.0 — every member of the cohort is alive — and declines monotonically to zero at the oldest age any member reaches. The slope of the curve at any age is determined by the mortality rate at that age: where the curve is shallow, few deaths occur per year; where it steepens, the cohort is contracting rapidly. The shape is approximately gradual through middle adult ages and bends sharply downward in advanced old age, reflecting the geometric rise of age-specific mortality. Concrete figures for a US female cohort starting at age 65: roughly 95% remain alive at 75, roughly 80% at 80, roughly 50% at 87, roughly 25% at 92, and roughly 5% at 98.
In practice
When an individual sees a survival curve in a retirement planning presentation or insurance illustration, two reference points carry most of the analytical weight: the age at which the curve crosses 50% — the median lifespan for the cohort, useful for understanding where the population center of mass sits — and the age at which the curve crosses 10% — the deep tail, useful for understanding what a conservative planning horizon would look like. A professional working with the curve should be able to explain which mortality table generated it, whether it incorporates projected mortality improvement, and which population the cohort represents. The shape of the curve is the direct visual representation of longevity risk: the wider the gap between the median and the tail, the more uncertain the individual's specific lifespan is.
In the Longevity Standard Framework
The survival curve is supporting vocabulary in the Longevity Standard framework, and the structural object on which every cost-of-income calculation operates. The frictionless pool benchmark, the solo drawdown baseline, the SPIA benchmark, and the DIA benchmark are all evaluated against the same survival curve — the curve determines how much income each premium dollar can fund at each planning horizon. The pooling multiplier is a direct consequence of the survival curve's shape: where the curve declines rapidly, per-survivor mortality credits become large, and the value of pooling rises with planning horizon. The structural pair of claim properties — risk sharing and adjustment mechanism — both operate on an arrangement's exposure to the survival curve.
Related terms
- Mortality rate
- Life expectancy
- Hazard rate
- Gompertz law
- Mortality table
- Cohort life table
- Longevity tail risk
- Maximum lifespan