Lifetime Asset Allocation with Idiosyncratic and Systematic Mortality Risks

Abstract

This paper considers the lifetime asset allocation problem with both idiosyncratic and systematic longevity risks, in which the stochastic mortality model is given by a general diffusion process. A wage earner can invest in a zero-coupon bond, a stock and a longevity bond, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton-Jacobi-Bellman equation. General solutions and special solutions are derived for the general diffusion mortality model and the square-root mortality model, respectively. To illustrate our results, numerical examples based on special solutions are provided. It is shown that idiosyncratic mortality risk has significant impacts on the wage earner’s investment, consumption, life insurance purchase and bequest decisions regardless of the length of the decision-making horizon, while systematic mortality risk only has significant impacts on the wage earner’s investment in the zero-coupon bond and the longevity bond. Since systematic mortality risk can be hedged by trading the longevity bond, its impacts on consumption, purchase of life insurance and bequest are not significant, especially when the decision-making horizon is short.