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

Zhen Wu and Zhenda Xu

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 21, 5356-5370

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.

Date: 2020
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DOI: 10.1080/03610926.2019.1618477

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