Merton’s Portfolio Optimization Problem in a Black & Scholes Market with Non-gaussian Stochastic Volatility of Ornstein-uhlenbeck Type
نویسندگان
چکیده
Abstract. We study Merton’s classical portfolio optimization problem for an investor who can trade in a risk-free bond and a stock. The goal of the investor is to allocate money so that her expected utility from terminal wealth is maximized. The special feature of the problem studied in this paper is the inclusion of stochastic volatility in the dynamics of the risky asset. The model we use is driven by a superposition of non-Gaussian OrnsteinUhlenbeck processes and it was recently proposed and intensively investigated for real market data by Barndorff-Nielsen and Shephard (2001). Using the dynamic programming method, explicit trading strategies and expressions for the value function via FeynmanKac formulas are derived and verified for power utilities. Some numerical examples are also presented.
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