Maximum principle for discrete-time control systems driven by fractional noises and related backward stochastic difference equations

Abstract

In this paper, motivated by stochastic control for systems driven by fractional Brownian motion and the applications for control problem with “colored noises” in real-world, the stochastic optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the “underlying” white noises. The solution of the backward stochastic difference equations is also investigated. As an application, the linear quadratic case is considered and an optimal investment problem is solved to illustrate the main results.