# Optimal Portfolio under Fast Mean-reverting Fractional Stochastic Environment

Jean-Pierre Fouque and Ruimeng Hu

Papers from arXiv.org

Abstract: 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 $H \in (\frac{1}{2}, 1)$. 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 rigorously 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 extend the discussions to general utility functions using the epsilon-martingale decomposition technique, and we obtain similar asymptotic optimality results within a specific family of admissible strategies.

New Economics Papers: this item is included in nep-upt
Date: 2017-06, Revised 2018-02
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