Portfolio Optimization Using Regime-Switching Stochastic Interest Rate and Stochastic Volatility Models

This paper considers the continuous-time portfolio optimization problem with both stochastic interest rate and stochastic volatility in regime-switching models, where a regime-switching Vasicek model is assumed for the interest rate and a regime-switching Heston model is assumed for the stock price.We use the dynamic programming approach to solve this stochastic optimal control problem. Under suitable assumptions, we prove a verification theorem.We then derive a closed-form solution of the associated Hamilton-Jacobi-Bellman (HJB) equation for a power utility function and a special choice of some model parameters. We prove the optimality of the closed-form solution by verifying the required conditions as stated in the verification theorem. We present a numerical example to show the optimal portfolio policies and value functions in different regimes.