Optimal Investment with Time-Varying Stochastic Endowments

Abstract

This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. We rely on the dynamic programming approach to solve the optimization problem. The properties of the value function, particularly the homogeneity, are used to reduce the HJB equation by one dimension. Furthermore, the optimal strategy is derived, and its asymptotic behavior is discussed.

Keywords: Utility maximization, Hamilton-Jacobi-Bellman equation, stochastic endowment, viscosity solution

JEL Classification: C61, G11