Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utility

摘要

In this paper, we assume that an investor can invest his/her wealth in a bond and a stock. In our wealth model, the stochastic interest rate is described by a Cox-Ingersoll-Ross (CIR) model, and the volatility of the stock is proportional to another CIR process. We obtain a closed-form expression of the optimal policy that maximizes a power utility. Moreover, a verification theorem without the usual Lipschitz assumptions is proved, and the relationships between the optimal policy and various parameters are given.