A NEW METHOD TO SOLVE THE HAMILTON-JACOBI-BELLMAN EQUATION FOR A STOCHASTIC PORTFOLIO OPTIMIZATION MODEL WITH BOUNDARY MEMORY

Abstract

Portfolio optimization problem with memory effect, namely, taking the past performance of portfolio into account, which is motivated by the fact that the decisions of the investors are influenced by the historic performance of the portfolio, has recently been of interest to researchers. Due to the memory effect, this type of problem is challenging. The main purpose of this paper is to propose a new approach to solve the Hamilton-Jacobi-Bellman (HJB) equation for the stochastic portfolio optimization model, which is more simple and generalized. We study the portfolio management problem under single investor and multi-investor framework. We establish certain conditions under which the problem can be reduced to the classical stochastic control problem and give some examples to show the advantages of our approach.