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

• 成果类型: Article
• 署名作者: Nie, Panpan; Wang, Guangchen; Wang, Yu
• 署名单位: Shandong University; Qilu Normal University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3244483
• 发表日期: 2023
• 页码: 6696-6710
• 关键词: Backward stochastic differential equation (BSDE); closed-loop representation of open-loop optimal control; Ekeland's variational principle; Pareto cooperative differential game; portfolio and consumption selection.

摘要

In this article, we are interested in studying a new kind of Pareto cooperative differential game of backward stochastic differential equation. Based on the 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 abovementioned theoretical results, a linear-quadratic game and a kind of optimal portfolio and consumption selection problem are also solved explicitly.