Dynkin Games with Incomplete and Asymmetric Information

• 成果类型: Article
• 署名作者: De Angelis, Tiziano; Ekstrom, Erik; Glover, Kristoffer
• 署名单位: University of Turin; Collegio Carlo Alberto; Uppsala University; University of Technology Sydney
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1141
• 发表日期: 2022
• 页码: 560-586
• 关键词: stochastic differential-games; Stopping games; INVESTMENT

摘要

We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian setup, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the other one (asymmetric information feature). We formulate the problem and reduce it to a fully Markovian setup where the uninformed player optimises over stopping times and the informed one uses randomised stopping times in order to hide their informational advantage. Then we provide a general verification result that allows us to find the value of the game and players' optimal strategies by solving suitable quasi-variational inequalities with some nonstandard constraints. Finally, we study an example with linear payoffs, in which an explicit solution of the corresponding quasi-variational inequalities can be obtained.