Mortality Table

Key takeaways

• A mortality table (life table or actuarial table) shows the probability that individuals in a defined population will die during a specified time interval.
• Insurers and government programs (e.g., Social Security) rely on mortality tables to set premiums, benefits, and assess long-term liabilities.
• Two main types exist: period life tables (snapshot of a specific time) and cohort/generation life tables (follow a birth cohort over its lifetime). Actuaries typically prefer cohort tables.
• Tables typically cover ages from birth to about 100 in one-year increments and may incorporate factors such as sex, smoking status, occupation, and socioeconomic class.

What is a mortality table?

A mortality table is a grid of probabilities that estimates the likelihood of death for members of a population at each age. It can show, for example, the chance that a person of a given age will die before their next birthday, or the survival rate from birth through later ages. These probabilities are used to calculate life expectancy, price life insurance, reserve funds, and value pension and social-insurance obligations.

How mortality tables work

Mortality tables are built from historical death and population data and adjusted for relevant characteristics. Typical features:
* Age-specific probabilities, usually expressed per 1,000 people or as a percentage.
* Separate construction for sexes and sometimes additional subgroups (smokers vs. non-smokers, occupations, weight classes, socioeconomic segments).
* One-year age increments, covering birth through old age (commonly up to 100).

Actuaries use these probabilities to model expected deaths over time, estimate expected claims, determine premiums, and ensure an insurer’s solvency by matching liabilities to assets.

Types of mortality tables

• Period life table: Represents mortality rates observed during a specific time period for a population. It provides a snapshot assuming current rates remain constant.
• Cohort (generation) life table: Follows a group born in the same period throughout their lives, incorporating projected changes in mortality over time. Because it captures generational improvements (or deteriorations) in survival, cohort tables are often preferred for actuarial work.

Data requirements and common metrics

Mortality tables require:
* Accurate counts of deaths and population by age and sex.
* Classification variables when producing subgroup tables (e.g., smoking status).
Common outputs:
* q_x — probability of dying between age x and x+1.
* l_x — number alive at age x out of an original cohort (used to compute survivors).
* Life expectancy at a given age.

Uses

• Life insurance: pricing policies, calculating reserves, and underwriting risk classes.
• Pensions and social insurance: projecting benefit payments and funding needs.
• Public health and demographic research: tracking population health and longevity trends.
• Risk assessment in finance and corporate planning.

Example

Mortality probabilities rise with age. For illustration:
* A newborn typically faces a very low probability of death in the first year and has a high remaining life expectancy.
* At extreme ages, the probability of dying within a year becomes large; historical life tables have shown very high annual mortality probabilities for centenarians.

(Actual probabilities depend on the specific table and cohort; for instance, some historical tables have indicated the annual death probability for a 119-year-old can exceed 90%.)

Brief history

Mortality tables date back centuries in demography and actuarial science. Modern statistical life tables were refined in the 19th and early 20th centuries; Raymond Pearl notably introduced mortality tables for ecological study in 1921.

Practical implications

Understanding which table type and variables apply is crucial: period tables are useful for short-term snapshots, while cohort tables better reflect long-term trends. Accurate mortality assumptions are essential for fair pricing, financial stability of insurers and pension plans, and meaningful demographic analysis.