Article
Version 2
This version is not peer-reviewed
Dynkin Game under G-Expectation in Continuous Time
Version 2
: Received: 11 May 2019 / Approved: 13 May 2019 / Online: 13 May 2019 (14:25:18 CEST)
How to cite: Wu, H.; Ren, Y.; Hu, F. Dynkin Game under G-Expectation in Continuous Time. Preprints 2019, 2019050106 Wu, H.; Ren, Y.; Hu, F. Dynkin Game under G-Expectation in Continuous Time. Preprints 2019, 2019050106
Abstract
In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.
Keywords
Dynkin game; Ambiguity; Backward stochastic differential equation (BSDE); Reflected backward stochastic differential equation (Reflected BSDE); Constraint
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment