Singular optimal control of a generalized backward doubly stochastic system with general jumps

In this paper, we study the singular optimal control problem of a generalized backward doubly stochastic system with general jumps. By the method of convex variation and duality technique, we establish sufficient and necessary maximum principles for the optimal control of such stochastic system. This result is a generalization of the maximum principles to singular optimal control problems for backward stochastic systems.