What is an actuarial life table?
An actuarial life table (also called a mortality table or life table) is a structured set of numbers that gives, for each age, the probability that a person of that age will die before their next birthday. Actuaries and insurers use these tables to estimate how long people of a given age are likely to live and to calculate the chance of surviving any particular next year of life.
Key definitions (plain language)
– Mortality rate (qx): the probability that a person aged x will die before their next birthday.
– Probability of surviving one year (px): 1 − qx.
– Remaining life expectancy (ex): the expected number of years a person aged x will live on average, based on the table.
– Period life table: a table built from mortality rates observed during a specific calendar period for a defined population. It reflects mortality at that time.
– Cohort (generation) life table: follows a group born in the same time window through their lifetimes (or models expected changes). It attempts to capture how mortality for that birth cohort will evolve over time.
– Actuary: a specialist who assesses financial risk using statistics and probability, often focused on mortality, morbidity, and financial consequences of uncertain future events.
How an actuarial life table works (conceptual)
– For each age, the table lists probabilities of death and survival for the following year.
– From those year-by-year probabilities, actuaries derive remaining life expectancy and the distribution of times-until-event (e.g., death, disability) needed for pricing and reserving.
– Tables are usually computed separately for men and women because historical mortality patterns differ by sex.
– Modern actuarial work can add adjustments (stratification) for additional risk factors such as smoking status, occupation, socio-economic group, or other behaviors to model different subpopulations.
Two main table types and why they matter
– Period life tables: good for describing mortality conditions during a particular year or short period. They are straightforward but do not account for future improvements (or deteriorations) in mortality.
– Cohort life tables: attempt to account for changing mortality over a cohort’s lifetime (for example, falling smoking rates or medical advances). They are useful when you want a table that reflects expected future changes in mortality for a birth cohort.
Common uses
– Life insurance pricing and reserves.
– Pension and annuity calculations (estimating how long payments will be needed).
– Public policy analysis (for example, Social Security plans).
– Scientific applications in biology and epidemiology.
– Product life-cycle management where human survival or replacement risk is relevant.
Practical checklist — what to check when you read or use a life table
– Population base: which population does the table describe (country, birth years, insured cohort)?
– Table type: period or cohort? (This affects whether future mortality changes are modeled.)
– Sex/sex-specific table: separate tables are common for males and females.
– Relevant adjustments: are there versions for smokers, occupation classes, or socio-economic categories?
– Date of the table: when were the underlying mortality rates measured or projected?
– Intended use: is the table appropriate for pricing, reserving, pension calculations, or demographic study?
Small worked example (hypothetical, simplified)
Suppose a life table entry for age 50 gives q50 = 0.0020. That means a 50-year-old has a 0.20% chance of dying before turning 51.
– One-year survival probability: p50 = 1 − q50 = 1 − 0.0020 = 0.9980 (99.80%).
– If you want a short, rough expected remaining life over the next three years only, you can add the probabilities of surviving each subsequent year (a simplified proxy for expected years lived in that 3-year window):
– Survive to 51: 0.9980
– Survive to 52: 0.9980 × (1 − q51). If q51 ≈ 0.0022, then survive to 52 ≈ 0.9980 × 0.9978 ≈ 0.9958
– Survive to 53: multiply again by (1 − q52). If q52 ≈ 0.0024, survive to 53 ≈ 0.9958 × 0.9976 ≈ 0.9935
– Expected years lived over ages 50–52 ≈ 1·(survive to 51) + 1·(survive to 52) + 1·(survive to 53) ≈ 0.9980 + 0.9958 + 0.9935 ≈ 2.9873 years
This gives an intuitive, truncated estimate for expected years in the next three years. Full remaining life expectancy uses the same idea extended over all future years and requires the whole table.
Notes on model granularity and data quality
– Older historical tables may undercount infant deaths; careful selection of the table is important for certain analyses.
– Insurers often use computerized predictive models to combine base mortality tables with underwriting factors (e.g., smoking, high-risk job) to create product-specific rates.
Sources for further reading
– Investopedia — Actuarial Life Table: https://www.investopedia.com/terms/a/actuarial-life-table.asp
– U.S. Social Security Administration — Actuarial Life Tables: https://www.ssa.gov/oact/STATS/table4c6.html (SSA maintains detailed tables and methodology notes)
– Society of Actuaries — Mortality and Longevity Research: https://www.soa.org/research/topics/mortality-longevity/
– National Association of Insurance Commissioners (NAIC) — Resources on life insurance and actuarial topics: https://www.naic.org/
Educational disclaimer
This explainer is educational only. It does not offer personalized financial, insurance, or investment advice. Use actual published life tables and a qualified actuary or financial professional when making decisions that depend on mortality or longevity assumptions.