Risk Modelling and Survival Analysis · Mortality projection

Approaches to Mortality Projection: Extrapolative, Explanatory and Expectation Methods

Updated 11 October 2026 · Fact-checked

Mortality projection forecasts future mortality rates. There are three approaches. Extrapolative methods continue past trends. Explanatory (process-based) methods model causes such as disease and risk factors. Expectation methods use expert opinion on future change. In exams, you describe each approach, then judge its strengths, limits and suitability for the stated purpose.

Understand Approaches to Mortality Projection

Insurers and pension schemes pay benefits many years ahead. If people live longer than assumed, annuities and pensions cost more. So you cannot just use today's mortality table. You need a view of how mortality rates will change. That is mortality projection.

There are three broad approaches in the CS2 course.

Extrapolative: you take past mortality data and extend the trend into the future. The simplest case is assuming the rate of improvement seen over recent years will continue. Lee-Carter and CBD are formal extrapolative models.
Explanatory (process-based): you model the causes of death, such as heart disease or cancer, and the risk factors behind them, such as smoking, diet and medical treatment. You project those factors and the effect on mortality.
Expectation: you ask experts, such as doctors, demographers and actuaries, what they think will happen. The view is a judgement, not a fitted model. Targets for future improvement often come from this approach.

Each approach answers a different question. Extrapolation asks, what has happened? Explanation asks, why did it happen and what will drive it next? Expectation asks, what do informed people believe will happen? Extrapolation is objective and cheap but assumes the past repeats. Explanation is more insightful but needs a lot of data and understanding. Expectation can capture new information but is subjective.

In practice, actuaries often blend approaches. For example, they may fit an extrapolative model, then adjust the long-term improvement rate using expert opinion. Uncertainty is large in every approach, so projections are often shown with ranges or scenarios.

Key rules to remember

Extrapolative idea (annual improvement): Improvement rate = 1 − q(x, t+1) ÷ q(x, t); A simple measure of year-on-year fall in the mortality rate at age x. Assuming it stays constant is a basic extrapolative method.
Projected rate with constant improvement: q(x, t+n) = q(x, t) × (1 − r)^n; Valid only if the improvement rate r is assumed constant at age x. State this assumption.
Three approaches: Extrapolative | Explanatory (process-based) | Expectation (expert opinion); Know the one-line definition, a strength and a limitation of each.

How to solve Approaches to Mortality Projection questions

Use this method for any question asking you to describe, compare or choose a projection approach.

1Read the question for the purpose: pricing annuities, reserving, pension funding, or a population forecast. This decides which approach fits.
2Name the approach you are discussing and define it in one sentence.
3Explain how it works in practice: what data and inputs it uses and what it produces.
4State the strengths, for example objectivity, simplicity, insight into causes, or use of current knowledge.
5State the limitations, for example assuming the past continues, data needs, subjectivity, or difficulty forecasting new risk factors.
6Link back to the question. Say which approach, or which blend, suits the purpose and why.
7Mention uncertainty, for example using scenarios, ranges or stochastic models, if the question allows.

Quickest way: Three-by-three grid

When to use it: Use it for short-answer and MCQ questions that ask you to compare or classify approaches.

Draw a mental grid: three approaches, and for each one a definition, a strength and a weakness.
Extrapolative: continues past trends; objective and simple; assumes the future resembles the past.
Explanatory: models causes and risk factors; gives insight into drivers; needs much data and is hard to project factors and their effects.
Expectation: expert judgement; can reflect new information; subjective and may be biased.
Match the question's clue words: trend or past data means extrapolative; causes or risk factors means explanatory; opinion or targets means expectation.

Common mistakes in Approaches to Mortality Projection

Calling Lee-Carter an explanatory model.
It has several parameters, so it looks like it explains mortality.
Fix: Lee-Carter fits age and time patterns to past data and extrapolates them. It is extrapolative. It does not model causes of death.
Listing strengths and limits without linking to the purpose.
Students memorise a list and write it out.
Fix: End each answer with a sentence saying which approach suits the stated use, for example long-term annuity reserving, and why.
Saying extrapolation is always reliable for short-term use.
Short horizons feel safer.
Fix: Say it tends to work better when trends are stable. It can fail if there is a structural change, such as a new treatment or a pandemic.
Treating expectation as having no basis.
It is subjective, so students dismiss it.
Fix: Experts use data, research and medical knowledge. The weakness is possible bias and lack of consistency, not that it is baseless.
Forgetting that the explanatory approach also needs projected inputs.
Students assume knowing the causes makes the forecast easy.
Fix: You must still forecast smoking rates, treatments and other factors, and how they affect mortality. This adds uncertainty.
Applying a constant improvement rate to all ages and all years without comment.
It makes the arithmetic simple.
Fix: State the assumption. Improvement rates differ by age and period, so say the result is only as good as that assumption.

Worked examples

Example 1

Describe the extrapolative approach to mortality projection. Give two advantages and two disadvantages. (5 marks)

Show the solution

Define: the extrapolative approach uses past mortality data to find trends in rates by age and time, then extends them into the future.
Advantage 1: it is objective and repeatable, because it relies on observed data rather than opinion.
Advantage 2: it is relatively simple and cheap to apply and can be fitted with standard models.
Disadvantage 1: it assumes past trends continue. It cannot anticipate new causes of death or medical advances.
Disadvantage 2: the result can depend on the data period chosen, and long-term projections have wide uncertainty.

Answer: Extrapolation extends observed trends. Advantages: objective and simple. Disadvantages: assumes the past continues and is sensitive to the data period and horizon.

Example 2

A mortality rate at age 70 is currently 0.020. An actuary assumes it improves by 2% a year, with a constant rate. Project the rate in 5 years. Name the approach and give one concern. (4 marks)

Show the solution

The method uses past trends extended forward, so it is extrapolative.
Use q(70, t+5) = q(70, t) × (1 − r)^5 with r = 0.02.
(0.98)^5 = 0.98² × 0.98² × 0.98 = 0.9604 × 0.9604 × 0.98 = 0.92237 × 0.98 = 0.90392.
Projected rate = 0.020 × 0.90392 = 0.018078, so about 0.0181.
Concern: the 2% rate is assumed constant. Real improvement may vary by period and could slow down or speed up.

Answer: The approach is extrapolative. Projected q(70) in 5 years is about 0.0181. The main concern is the constant improvement assumption.

Exam tips

Use the exact terms: extrapolative, explanatory (process-based) and expectation. Examiners mark against these.
For 'discuss' questions, give both strengths and limitations. One-sided answers lose marks.
Tie your conclusion to the purpose, for example annuity pricing or pension funding.
Where a calculation uses a constant improvement rate, write the assumption explicitly.
In MCQs, match clue words: past trend, cause or risk factor, expert opinion.

Practice questions from Mortality projection

Approaches to Mortality Projection: frequently asked questions

What is the difference between extrapolative and explanatory mortality projection?

Extrapolative methods extend observed past trends in mortality rates. Explanatory methods model the causes of death and the risk factors behind them. Extrapolation tells you what happened. Explanation tries to tell you why.

Is the expectation approach a statistical model?

Not usually. It relies on expert judgement about future change, often informed by data and medical knowledge. It can be used alone or to adjust the results of a model.

Which approach do actuaries use most?

Extrapolative models are widely used because they are objective and practical. Actuaries often add expert judgement, particularly for long-term improvement. The choice depends on purpose and available data.

Is Lee-Carter extrapolative?

Yes. It fits age and time patterns in past mortality and projects the time component forward. It does not model causes of death.