Stochastic Mortality Under Measure Changes

Enrico Biffis, Michel Denuit and Pierre Devolder

We provide a self-contained analysis of a class of continuous-time stochastic
mortality models that have gained popularity in the last few years. We describe
some of their advantages and limitations, examining whether their features
survive equivalent changes of measures. This is important when using the same
model for both market-consistent valuation and risk manage- ment of life insurance
liabilities. We provide a numerical example based on the calibration to the French
annuity market of a risk-neutral version of the model proposed by Lee and Carter (1992).

Key words and phrases: stochastic mortality, Lee-Carter model, mortality risk premium, fair
valuation, mortality-linked securities.

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