Applied Mathematics & Information Sciences

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This paper considers that the goal of the fund manager is to minimize the expected utility loss function, and the noises involved with the dynamics of some wealth are fractional Brownian motions with short-ranged dependence. By applying Hamilton and Lagrange multiplier, the stochastic optimal control problem is converted into non-random optimization. Furthermore, based on deterministic optimal control principle, it obtains the explicit solution of the optimal strategies via moment equations. Finally, it presents a simulation to analyze the dynamic behaviour of the optimal portfolio strategy influenced by the orders of fractional Brownian motions.

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