摘要：This paper considers a portfolio optimization problem with delay. The finance market is consisted of one risk-free asset and one risk asset which price process is modeled by Cox-Ingersoll-Ross stochastic volatility model. In addition, considering the history information related to investment performance, the dynamic of wealth is modeled by stochastic delay differential equation. The investor’s objective is to maximize her expected utility for a linear combination of the terminal wealth and the average performance. By applying stochastic dynamic programming approach, we provide the corresponding Hamilton-Jacobin-Bellman equation and verification theorem, and the closed-form expressions of optimal strategy and optimal value function for CRRA utility are derived. Finally, a numerical example is provided to show our results.
