ON THE ROBUST DYNKIN GAME

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Ya, Song
• 署名单位: University of Michigan System; University of Michigan; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1243
• 发表日期: 2017
• 页码: 1702-1755
• 关键词: stochastic differential-games; sum stopping games; reflected bsdes; Singular control; 2 barriers; EQUATIONS; american

摘要

We analyze a robust version of the Dynkin game over a set P of mutually singular probabilities. We first prove that conservative player's lower and upper value coincide (let us denote the value by V). Such a result connects' the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process V is a submartingale under an appropriately defined nonlinear expectation E up to the first time tau* when V meets the lower payoff process L. If the probability set P is weakly compact, one can even find an optimal triplet (P*, tau*, gamma*,) for the value V-0. The mutual singularity of probabilities in P causes major technical difficulties. To deal with them, we use some new methods including two approximations with respect to the set of stopping times.