Pareto optimality of stochastic delay systems in finite horizon

In this paper, we present necessary as well as sufficient conditions for Pareto optimality of delayed stochastic cooperative differential game in finite horizon. The problem is transformed into a set of constrained delayed stochastic optimal control problems. Based on the maximum principle for stochastic delay optimal control problem with state constraints, we obtain the necessary condition for the existence of the Pareto efficient strategy, and then a sufficient verification theorem is given under certain convex assumptions. To explain the theoretical results, we apply them to an indefinite linear quadratic (LQ) problem. By introducing the relaxed compensators, all Pareto efficient strategies can be obtained by the weighted sum optimality method.