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

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  • Zhen Wu
  • Zhenda Xu

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.

Suggested Citation

  • Zhen Wu & Zhenda Xu, 2020. "A kind of stochastic recursive Zero-Sum differential game problem with double obstacles constraint," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(21), pages 5356-5370, November.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:21:p:5356-5370
    DOI: 10.1080/03610926.2019.1618477
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