Portfolio Optimization for Assets with Stochastic Yields and Stochastic Volatility

In this paper, we consider a stochastic portfolio optimization model for investment on a risky asset with stochastic yields and stochastic volatility. The problem is formulated as a stochastic control problem, and the goal is to choose the optimal investment and consumption controls to maximize the investor's expected total discounted utility. The Hamilton-Jacobi-Bellman equation is derived by virtue of the dynamic programming principle, which is a second-order nonlinear equation. Using the subsolution-supersolution method, we establish the existence result of the classical solution of the equation. Finally, we verify that the solution is equal to the value function and derive and verify the optimal investment and consumption controls.