Optimal Portfolio Strategies with Mispricing and Stochastic Volatility

This paper investigates an optimal portfolio selection problem in a market with mispricing and stochastic volatility. The investor's objective is to maximize the expected power utility of the terminal wealth, and the financial market consists of one risk-free asset, one risky asset representing the market index, and a pair of stocks whose prices are mispriced. Meanwhile, the volatilities of the market index and system risk are described by Heston stochastic volatility model. Without/with limited short selling constraints, the closed-form expressions of the optimal strategies and the optimal value functions are derived by the dynamic programming approach and the Lagrange multiple method. Moreover, economic implications and numerical examples are provided to illustrate that how the investment horizon and mispricing error affect the optimal strategies.