Optimal Portfolio under Fractional Stochastic Environment

Rough stochastic volatility models have attracted lots of attention recently. In this paper, for power-type utilities, we propose to use martingale distortion transformations for the optimal value of asset allocation... [ view full abstract ]

Rough stochastic volatility models have attracted lots of attention recently. In this paper, for power-type utilities, we propose to use martingale distortion transformations for the optimal value of asset allocation problems in a (non-Markovian) fractional stochastic environment. We rigorously establish first order approximations of the optimal value and the optimal strategy, when the return and volatility are driven by a stationary slowly varying fractional Ornstein-Uhlenbeck process. We prove that this approximation can be also generated by a zeroth-order trading strategy providing an explicit strategy which is asymptotically optimal in all admissible controls. We extend the discussion to general utility functions.