A kind of stochastic recursive Zero-Sum differential game problem with double obstacles constraint

Abstract

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.