Threshold Life Tables and Their Applications

Abstract

The rapid emergence of centenarians has highlighted the importance of survival probabilities at extreme ages and has motivated actuaries to look for alternative ways to close of life tables in place of assigning a death probability of 1 at an arbitrarily chosen age. Using the asymptotic results of modern extreme value theory, we propose a model, which we call the threshold life table, to extrapolate survival distributions to extreme ages and to determine the appropriate end point of a life table. By combining the threshold life table with the Lee-Carter model for stochastic mortality forecasting, we consider applications to the valuation of a life annuity portfolio and to the prediction of the highest attained age. We illustrate the theoretical results using U.S., Canadian, and Japanese mortality data.