A general stochastic maximum principle for discrete‐time mean‐field optimal controls

Abstract

AbstractThis paper deals with the discrete‐time mean‐field stochastic optimal control problem under weakened convexity assumption. By introducing the concept of the ‐convex set, a special variation of the control is proposed. Using the new discrete‐time backward stochastic equation of mean‐field type, the global stochastic maximum principle is established. Moreover, as illustrations, one kind of discrete‐time linear‐quadratic (LQ) nonzero‐sum stochastic game and a discrete‐time mean‐variance portfolio selection optimization problem are solved.