A Maximum Principle for Discrete Delayed Stochastic Control System Driven by Fractional Noise

In this paper, we study optimal control problem of discrete stochastic control system with delays. Distinct from the existing works, the control system is driven by fractional noise and the Malliavin duality formula is applied to deal with the fractional terms. The admissible control domain is not necessarily convex. We establish a maximum principle of general type by classical variation method and simplify it by constructing a pair of discrete backward stochastic difference equations as the adjoint equations. A linear quadratic optimal control problem is solved to clarify the main result as an application.