STOCHASTIC PERRON FOR STOCHASTIC TARGET GAMES

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Li, Jiaqi
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1112
• 发表日期: 2016
• 页码: 1082-1110
• 关键词: viscosity solutions; verification; EQUATIONS

摘要

We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solution (super-solution) of a Hamilton-Jacobi-Bellman (HJB) equation. We then characterize the value function as a viscosity solution to the HJB equation using a comparison result and a byproduct to obtain the dynamic programming principle.