论文标题
关于具有部分和不对称信息的非马克维亚dynkin游戏的价值
On the value of non-Markovian Dynkin games with partial and asymmetric information
论文作者
论文摘要
我们证明，零和dynkin游戏连续时间与部分和非对称信息接纳在随机停止时间中的价值，而播放器的停止收益是一般\ cadlag可测量的过程。作为我们的证明方法的副产品，我们还为两个参与者提供了最佳策略。主要的新事迹是，我们不假定游戏的马尔可夫性质，也不是玩家可用的信息的特定结构。这使我们能够超越文献中关于Dynkin Games的变异方法（基于PDE），并与部分/不对称信息相连。取而代之的是，我们关注基于随机过程的一般理论和Sion的Min-Max定理的概率和功能分析方法（M. Sion，Pacific J. Math。，8，1958，第171-176页）。我们的框架包括有关连续时间Dynkin游戏中使用不对称信息的文献中发现的示例，我们提供反例，以表明我们的假设不能进一步放松。
We prove that zero-sum Dynkin games in continuous time with partial and asymmetric information admit a value in randomised stopping times when the stopping payoffs of the players are general \cadlag measurable processes. As a by-product of our method of proof we also obtain existence of optimal strategies for both players. The main novelties are that we do not assume a Markovian nature of the game nor a particular structure of the information available to the players. This allows us to go beyond the variational methods (based on PDEs) developed in the literature on Dynkin games in continuous time with partial/asymmetric information. Instead, we focus on a probabilistic and functional analytic approach based on the general theory of stochastic processes and Sion's min-max theorem (M. Sion, Pacific J. Math., 8, 1958, pp. 171-176). Our framework encompasses examples found in the literature on continuous time Dynkin games with asymmetric information and we provide counterexamples to show that our assumptions cannot be further relaxed.
