Distribution of the random future life expectancies in log-bilinear mortality projection models

Projected life tables are obtained from forecasting methods and account for future improvements in longevity. Since the future path of mortality is unknown, working with projected life tables makes the survival probabilities stochastic. The resulting demographic indicators in turn become random variables. This paper aims to study the distribution of period and cohort life expectancies derived from projected life tables. To fix the ideas, we adopt here the standard Lee-Carter framework, where the future forces of mortality are decomposed in a log-bilinear way. Exact formulas are derived for period life expectancies, and approximations are proposed for cohort life expectancies. In the latter case, numerical illustrations based on Belgian population data show that the relative accuracy is remarkable.