STOCHASTIC DIFFERENTIAL GAMES WITH RANDOM COEFFICIENTS AND STOCHASTIC HAMILTON-JACOBI-BELLMAN-ISAACS EQUATIONS

• 成果类型: Article
• 署名作者: Qiu, Jinniao; Zhang, Jing
• 署名单位: University of Calgary; Fudan University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1831
• 发表日期: 2023
• 页码: 689-730
• 关键词: viscosity solutions; backward sdes

摘要

In this paper, we study a class of zero-sum two-player stochastic differ-ential games with the controlled stochastic differential equations and the pay-off/cost functionals of recursive type. As opposed to the pioneering work by Fleming and Souganidis [Indiana Univ. Math. J. 38 (1989) 293-314] and the seminal work by Buckdahn and Li [SIAM J. Control Optim. 47 (2008) 444- 475], the involved coefficients may be random, going beyond the Markovian framework and leading to the random upper and lower value functions. We first prove the dynamic programming principle for the game, and then un-der the standard Lipschitz continuity assumptions on the coefficients, the up-per and lower value functions are shown to be the viscosity solutions of the upper and the lower fully nonlinear stochastic Hamilton-Jacobi-Bellman- Isaacs (HJBI) equations, respectively. A stability property of viscosity solu-tions is also proved. Under certain additional regularity assumptions on the diffusion coefficient, the uniqueness of the viscosity solution is addressed as well.