Optimal Portfolio Selection under the Short-range Fractional Brownian Motion

Abstract

In this paper, we study the classical portfolio selection problem and extend the Brownian motion about the noises involved in the dynamics of wealth to a short-range fractional Brownian motion. Instead of using the classical tool of optimal control as optimization engine, we convert the stochastic optimal control problem into a non-random optimization by using Hamilton and Lagrange multiplier, and conclude the solution of the initial problem. Based on deterministic optimal control principle, we obtain the explicit solution of the optimal strategies. Finally, we present a simulation and analyze the sensitivity of the fractional order to the optimal strategy.