Profit testing of profit sharing life insurance policies when asset returns are variance gamma distributed

Abstract

This paper examines the profit testing of life insurance companies that issue participating policies, type B and type A universal life policies, and variable annuities with guaranteed minimum maturity and death benefits, when investment returns are stochastic and modeled by normal or variance gamma distributions. We rely on the stochastic profit testing techniques introduced in Dickson et al. (Actuarial mathematics for life contingent risks, 2nd edn, Cambridge University Press, Cambridge, 2013) to examine the influence of the models’ parameters and of the models themselves on the profit testing indicators. We show that the variance gamma model results in more conservative predictions than the normal model for most cases.