Empirical studies indicate the existence of long range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein-Uhlenbeck (fOU) process with Hurst index H ∈ ( 1 2 , 1). In this paper, we analyze the nonlinear optimal portfolio allocation problem under this model and in the regime where the fOU process is fast mean-reverting. We first consider the case of power utility, and

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... ly give first order approximations of the value and the optimal strategy by a martingale distortion transformation. We also establish the asymptotic optimality in all admissible controls of a zeroth order trading strategy. Then, we consider the case with general utility functions using the epsilon-martingale decomposition technique, and we obtain similar asymptotic optimality results within a specific family of admissible strategies. . Here, ǫ is a small parameter to make the process Y ǫ,H t fast-varying and its natural time scale to be of order ǫ (that is, its mean-reversion time scale proportional to ǫ), and W (H) t is a fractional Brownian motion