2017/06/09 by Jean‐Pierre Fouque, Ruimeng Hu, Fouque, Jean-Pierre +1
Economics, Econometrics and Finance · #60G22 #91G10 #93E20 #Economic theories and models #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Portfolio Management (q-fin.PM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1706.03139
openalex publication_date 2017/06/09 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
Empirical studies indicate the existence of long range dependence in the\nvolatility of the underlying asset. This feature can be captured by modeling\nits return and volatility using functions of a stationary fractional\nOrnstein--Uhlenbeck (fOU) process with Hurst index H \∈ (\(1)/(2), 1). In\nthis paper, we analyze the nonlinear optimal portfolio allocation problem under\nthis model and in the regime where the fOU process is fast mean-reverting. We\nfirst consider the case of power utility, and rigorously give first order\napproximations of the value and the optimal strategy by a martingale distortion\ntransformation. We also establish the asymptotic optimality in all admissible\ncontrols of a zeroth order trading strategy. Then, we extend the discussions to\ngeneral utility functions using the epsilon-martingale decomposition technique,\nand we obtain similar asymptotic optimality results within a specific family of\nadmissible strategies.\n