Optimization and Asset Allocation Under Uncertain Lifetime

Abstract

This paper studies the optimal decisions on investment, consumption, and annuitization strategy of the retiree with an uncertain lifetime. The model introduced by Milevsky in 2007 is followed and obtain analytical solutions by using the substitution method to solve the Hamilton Jacobi Bellman equation. A numerical example is providing to show the effect of the pensioner’s decision model. Different with the current literature, this study analyzed the effect of variety model parameters on the optimal utility and found that the individual’s optimal utility depends on the initial wealth, investment volatility and time of death after retirement. This study also observes that investment volatility has a negative effect on the pensioner’s decision on optimal utility.