Necessary and Sufficient Conditions for Pareto Optimal Solution of Backward Stochastic System With Application

Abstract

This paper is interested in studying a new kind of Pareto cooperative differential game of backward stochastic differential equation. Based on characterizations of Pareto optimal solution, the game problem is transformed into a set of single objective optimal control problems with constraints of backward stochastic differential equations. In the first place, a necessary condition for Pareto optimal strategy is established by virtue of Ekeland's variational principle, and then it is proved that the necessary condition is also sufficient under certain convex assumption. To shed light on the application of the above theoretical results, a linear-quadratic game and a kind of optimal portfolio and consumption selection problem are also solved explicitly.