Actuarial Basics — Mortality Tables, Life Expectancy & Premium Pricing
What actuaries do in a life insurer, how a mortality table is read and used to work out expected claims, why a level premium builds a reserve, what adverse selection is, and the role of the Appointed Actuary.
What actuarial work is
Actuarial science applies mathematics and statistics to measure insurance risk. In life insurance, actuaries price products, value the reserves an insurer must hold for future claims and report on its financial soundness.
The starting point is that no one can say when a particular person will die, but in a large group the number of deaths in a year can be estimated closely. Pricing rests on the group, not on the individual.
Mortality tables
A mortality table shows the probability of death at each age. Multiplying that probability by the number of lives at that age gives the expected number of deaths in a year, and multiplying again by the sum assured gives the expected claims.
In India the Indian Assured Lives Mortality (IALM) tables are published by the Institute of Actuaries of India from time to time. They reflect the mortality experience of insured lives, not of the whole population. Insured lives tend to show lower mortality because they were medically underwritten when their policies were issued, an effect known as selection.
The level premium and the reserve
The cost of mortality rises with age. If premiums followed that cost exactly, they would be low in the early years and climb every year. A level premium instead keeps the premium the same in every year of the term: the actuary spreads the rising cost evenly over the premium-paying term, using present-value techniques.
The consequence is that early premiums exceed the cost of cover in those years, and later premiums fall short of it. The early excess is not profit. It builds a reserve that the insurer holds to meet the higher cost of the later years.
Adverse selection and the Appointed Actuary
Adverse selection is the tendency of people who know they are at higher risk to buy insurance, or more of it, than people at lower risk. Unchecked, it makes the insured group riskier than the insurer assumed in its pricing. Underwriting, through health questions and medical tests, is how insurers identify and price such risks.
Every life insurer is required to have an Appointed Actuary. This is an officer of the insurer who answers to its Board and to IRDAI, which receives the Appointed Actuary's annual report. The duty is to protect policyholders' interests, for example by certifying that reserves are adequate.
Rules at a glance
Why the same premium at 30 and at 55
Illustration: Imran takes a 30-year term plan at 30 with a level premium. At 31 his premium is more than the cost of covering him for that year; at 58 the same premium is less than the cost of covering a 58-year-old. The insurer has held the early excess in reserve to pay for the later shortfall.
His colleague, who has just been told of a serious heart condition, wants to buy a large policy at once. That is the pattern adverse selection describes, and it is why the proposal form asks health questions and the insurer may call for medical tests before deciding its terms.
From a mortality rate to a level premium
- Assumptions, for arithmetic only: a group of 20,000 policyholders, all males aged 45; an assumed mortality rate of 3.5 per 1,000 lives for the year; a sum assured of ₹10,00,000 on each life. The rate is not taken from any published table.
- Expected deaths = 20,000 × 3.5 ÷ 1,000 = 70.
- Expected claims = 70 × ₹10,00,000 = ₹7,00,00,000.
- Pure mortality cost per policyholder for the year = ₹7,00,00,000 ÷ 20,000 = ₹3,500, before expenses, investment income and margins.
- The level-premium idea, on separate invented figures and ignoring interest and deaths: suppose the cost of cover is ₹3,000 in year 1, ₹4,000 in year 2 and ₹5,000 in year 3. Total = ₹12,000, so a level premium is ₹12,000 ÷ 3 = ₹4,000 a year.
- Year 1 leaves an excess of ₹4,000 − ₹3,000 = ₹1,000, which is held in reserve; year 2 breaks even; year 3 has a shortfall of ₹5,000 − ₹4,000 = ₹1,000, met from the reserve.
Result. The group is expected to produce 70 deaths and ₹7 crore of claims, a pure cost of ₹3,500 a life. In the three-year sketch a level ₹4,000 overpays by ₹1,000 early and uses it later.
Key points
- Actuaries price products, value reserves and report on an insurer's financial soundness.
- A mortality table gives the probability of death at each age.
- IALM tables reflect the experience of insured lives in India, not of the general population.
- Expected deaths = number of lives × mortality rate.
- A level premium stays the same every year; early premiums exceed the cost of cover and build a reserve.
- Adverse selection is the tendency of higher-risk people to buy more cover; underwriting is the check on it.
- The Appointed Actuary is accountable to the insurer's Board and to IRDAI.
Common misunderstandings
- IALM tables do not describe the general population: they reflect insured lives, who were underwritten when they bought cover.
- The early excess in a level premium is not the insurer's profit: it builds the reserve for the costlier later years.
- A level premium does not mean the risk is level: the cost of mortality rises with age, and the premium is an average over the term.
- Adverse selection is not the same as fraud: it describes who tends to buy cover, and underwriting is how insurers price for it.
- The Appointed Actuary does not answer to the Board alone: the role is also accountable to IRDAI.
Questions people ask
Why do insured lives show lower mortality than the general population?
Because they were medically underwritten when their policies were issued. The effect is known as selection.
Does a mortality rate say when a given person will die?
No. It gives a probability for a group at an age. It is used to estimate the number of deaths in a large group, not the fate of one person.
Who publishes the IALM tables?
The Institute of Actuaries of India, from time to time.
What is the Appointed Actuary's duty?
To protect policyholders' interests, for example by certifying that the insurer's reserves are adequate, and to report to the Board and to IRDAI.
What this lesson relies on
- Indian Assured Lives Mortality (IALM) tables — Institute of Actuaries of India
- IRDAI's requirement that every life insurer have an Appointed Actuary, who reports to the Board and to IRDAI
This lesson was reviewed independently against these sources on 8 October 2026. Rules change: check the current regulation, scheme document or policy wording before relying on any figure. This is education, not advice.