Optimal portfolio for multi-asset in a jump-diffusion model with time-varying market structure

Abstract

An optimal portfolio problem for an investor who can invest his wealth in stock, bond and cash account is considered in a jump-diffusion model with time-varying market structure, where the short nominal interest rates, the inflation uncertainty and the excess return of stock are all assumed to follow mean-reverting stochastic processes. Guided by stochastic dynamic programming principle, we gain a Hamilton-Jacobi-Bellman(HJB) equation which corresponds to the optimal portfolio strategies. In addition, we determine the portfolio choice, and illustrate the behaviors of investment strategy to stock by examining the impacts of jumps, risk aversion parameters and different investment time horizons with numerical examples in the case of constant relative risk aversion (CRRA) utility function and the jump-sizes following double exponential distribution.