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Optimal Portfolio under Fast Mean-Reverting Fractional Stochastic Environment
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, anddoi:10.1137/17m1134068 fatcat:7o2qyh2s4nev3fdhdqloqobigu