Working Paper Article Version 2 This version is not peer-reviewed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.

## Subject Areas

Dynkin game; Ambiguity; Backward stochastic differential equation (BSDE); Reflected backward stochastic differential equation (Reflected BSDE); Constraint

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