Mean-variance longevity risk-sharing for annuity contracts

Abstract

This paper investigates longevity risk-sharing as a solution to the sustainability and affordability problems in the annuity market, and in particular how much longevity risk could be transferred back to policyholders assuming mean-variance preference functions. First, it provides dynamic risk-sharing rules for annuities. Second, it studies the contract properties from the perspectives of both the provider and individual policyholders. Third, it highlights and accounts for two levels of uncertainty and two levels of correlation induced by systematic longevity risk. Fourth, it provides necessary and sufficient conditions on the premium loading and the share of transferred risk, such that both parties prefer risk-sharing. The analytical and numerical results of the paper offer a deeper understanding of the effects of systematic and diversifiable risks on those preferences, and show that the products presented in this paper are suitable retirement solutions.