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In this paper, we study the portfolio optimization problem under an extended Heston stochastic volatility model. By using asymptotic analysis technique, we are able to derive approximations of the optimal value function and the optimal strategy. We give an explicit asymptotic approximation of the optimal strategy for the case of hyperbolic absolute risk aversion utility functions and prove that the leading order term of the optimal strategy recovers the approximation up to the first order of the optimal value function. AMS Subject Classification: 90C39, 90C59, 91G10, 35Q93

ASYMPTOTIC ANALYSIS FOR PORTFOLIO OPTIMIZATION PROBLEM UNDER AN EXTENDED HESTON'S STOCHASTIC VOLATILITY MODEL