How Life Tables Power Insurance Pricing and Risk Assessment

Life tables are a core tool in actuarial science used to describe the survival and death probabilities of a specific population. By modeling these probabilities, insurers can compute expected lifespans, mortality rates, and other key actuarial metrics essential for setting premiums, evaluating risk, and determining reserves.

Life Table Model

1. Survival Function

Survival Function (S(x)) represents the probability that an individual aged x will survive to at least age x + t.

The survival function is non‑increasing, decreasing as age increases.

The survival function can be expressed as:

where l(x) is the number of survivors at age x and l(0) is the initial cohort (usually 100,000).

2. Mortality Rate

Mortality Rate (q(x)) denotes the probability that a person aged x will die between ages x and x + 1.

The mortality rate can be calculated as:

where d(x) is the number of deaths at age x.

3. Life Expectancy

Life Expectancy (e(x)) indicates the expected remaining years of life for an individual aged x.

Life expectancy is derived from the survival function by integrating (or summing) the survival probabilities over future ages.

4. Complete Life Table

A complete life table typically includes the following columns:

Age (x)

Number of survivors l(x)

Number of deaths d(x)

Mortality rate q(x)

Life expectancy e(x)

Example data:

Age | Survivors | Deaths | Mortality Rate | Life Expectancy

0 | 100,000 | 500 | 0.005 | 75.0

1 | 99,500 | 50 | 0.0005 | 74.2

2 | 99,450 | 30 | 0.0003 | 73.3

Case Study

Assume a cohort of 100,000 newborns. Using the model, we calculate survival rates, mortality rates, and life expectancy for each age group.

For ages 0‑1, if 500 deaths occur, the survival function is computed accordingly, and the mortality rate follows from the deaths and survivors.

The calculation of life expectancy involves integrating the survival function, often requiring numerical methods. For example, if the remaining life expectancy at age 0 is estimated at 45 years, this figure informs pricing and reserve calculations for a life‑insurance product targeting 30‑year‑old males.

By leveraging survival functions, mortality rates, and life expectancy, life tables provide insurers with critical data for scientific risk assessment and product pricing, and they are also applicable to demography and public health.