Optimal Portfolio under Fast Mean-Reverting Fractional Stochastic Environment

Jean-Pierre Fouque, Ruimeng Hu
2018 SIAM Journal on Financial Mathematics  
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
more » ... 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
doi:10.1137/17m1134068 fatcat:7o2qyh2s4nev3fdhdqloqobigu