A General Maximum Principle for Discrete Fractional Stochastic Control System of Mean‐Field Type

Abstract

In this paper, we investigate a general maximum principle for discrete fractional stochastic difference system of mean‐field type. The admissible control domain is nonconvex. We give Malliavin calculus for discrete‐time case to deal with the fractional terms. The maximum principle of general type is derived by classical variation and linear operator methods. In addition, a linear‐quadratic problem is solved to illustrate the main result and we also figure out a numerical result in this case.