A Poisson log-bilinear regression approach to the construction of projected lifetables

This paper implements Wilmoth’s [Computational methods for fitting and extrapolating the Lee–Carter model of mortality change, Technical report, Department of Demography, University of California, Berkeley] and Alho’s [North American Actuarial Journal 4 (2000) 91] recommendation for improving the Lee–Carter approach to the forecasting of demographic components. Specifically, the original method is embedded in a Poisson regression model, which is perfectly suited for age–sex-specific mortality rates. This model is fitted for each sex to a set of age-specific Belgian death rates. A time-varying index of mortality is forecasted in an ARIMA framework. These forecasts are used to generate projected age-specific mortality rates, life expectancies and life annuities net single premiums. Finally, a Brass-type relational model is proposed to adapt the projections to the annuitants population, allowing for estimating the cost of adverse selection in the Belgian whole life annuity market.