IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
A pension insurer projects mortality using a stochastic model and finds that the width of the prediction interval for the value of a portfolio of annuities hardly narrows when the number of annuitants rises from 10,000 to 1,000,000. What is the most likely explanation?
The remaining uncertainty is systematic: future mortality trend and parameter estimation error affect every annuitant simultaneously, so they do not diversify. Only independent process risk shrinks as the portfolio grows, which is why the interval barely narrows.
- AThe uncertainty is dominated by systematic risk from future mortality trend and parameter uncertainty, which affects all annuitants together and does not diversifyCorrect
- BThe process risk per life has increased with portfolio size
- CThe model has too many age-specific parameters, which causes independence of lives
- DThe central limit theorem fails for portfolios of annuitants above 10,000 lives
- Prediction intervals for annuity values depend only on the interest rate assumption
Explanation
Idiosyncratic (process) risk reduces in relative terms as the number of independent lives grows. Uncertainty about trend and parameters is common to all lives, so it remains however large the portfolio. This is why longevity risk is not removed by pooling alone.
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