Stochastic Optimal Control of DC Pension Fund under the Fractional Brownian Motion

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