An Optimal Equity-Linked Pure Endowment Contract: Optimal Stochastic Control

Abstract

This article studies pure-endowment contracts whose investments are funded simultaneously in risk-free and risky financial markets. Using the optimal stochastic control method and the assumption that the jumps of the risky financial market follow either finite or infinite activity Lévy process, and that the policyholder’s utility function is a CRRA utility function, it derives an optimal investment strategy and optimal policyholder consumption, which depends on the mortality rate. Several mortality models and jump parameters are employed to study the sensitivity of our findings. 2010 AMS Classifications: 62P05, 91B30, 93E20