We study reflected backward stochastic differential equations (RBSDEs) on the probability space equipped with a Brownian motion. The main novelty of the paper lies in the fact that we consider the following weak assumptions on the data: barriers are optional of class (D) satisfying weak Mokobodzki’s condition, generator is continuous and non-increasing with respect to the value-variable (no restrictions on the growth) and Lipschitz continuous with respect to the control-variable, and the terminal condition and the generator at zero are supposed to be merely integrable. We prove that under these conditions on the data there exists a solution to corresponding RBSDE. In the second part of the paper, we apply the theory of RBSDEs to solve basic problems in Dynkin games driven by nonlinear expectation based on the generator mentioned above. We prove that the main component of a solution to RBSDE represents the value process in corresponding extended nonlinear Dynkin game. Moreover, we provide sufficient conditions on the barriers guaranteeing the existence of the value for nonlinear Dynkin games and the existence of a saddle point.

我们研究配备布朗运动的概率空间上的反射后向随机微分方程（RBSDE）。本文的主要新颖之处在于我们考虑了以下对数据的弱假设：障碍是满足弱 Mokobodzki 条件的类 (D) 的可选，生成器相对于值变量是连续且非递增的（无增长的限制）和关于控制变量的 Lipschitz 连续，并且终端条件和为零的生成器应该只是可积的。我们证明在这些数据条件下，存在相应的 RBSDE 解。在本文的第二部分中，我们应用RBSDE理论来解决基于上述生成器的非线性期望驱动的Dynkin博弈的基本问题。我们证明了 RBSDE 解的主要组成部分代表了相应的扩展非线性 Dynkin 博弈中的价值过程。此外，我们还提供了保证非线性 Dynkin 博弈值存在和鞍点存在的障碍的充分条件。