标题：A kind of stochastic recursive Zero-Sum differential game problem with double obstacles constraint
作者：Wu, Zhen; Xu, Zhenda
作者机构：[Wu, Zhen] Shandong Univ, Sch Math, Jinan, Shandong, Peoples R China.; [Xu, Zhenda] Shandong Univ, Zhongtai Secur Inst Financial Studies, Jinan 2501 更多
通讯作者地址：[Xu, ZD]Shandong Univ, Zhongtai Secur Inst Financial Studies, Jinan 250100, Peoples R China.
来源：COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
关键词：stochastic zero-sum differential game; recursive utility; mixed; differential game; doubly reflected backward stochastic differential; equation; sufficient condition
摘要：This paper concerns a class of stochastic recursive zero-sum differential game problem with recursive utility related to a backward stochastic differential equation (BSDE) with double obstacles. A sufficient condition is provided to obtain the saddle-point strategy under some assumptions. In virtue of the corresponding relationship of doubly reflected BSDE and mixed game problem, a stochastic linear recursive mixed differential game problem is studied to apply our theoretical result, and here the explicit saddle-point strategy as well as the saddle-point stopping time for the mixed game problem are obtained. Besides, a numeral example is also given to demonstrate the result by virtue of partial differential equations (PDEs) computation method.