论文标题
非线性BSDE具有两个可选的DOOB的类障碍，满足了Mokobodzki的状况和扩展Dynkin游戏
Nonlinear BSDEs with two optional Doob's class barriers satisfying weak Mokobodzki's condition and extended Dynkin games
论文作者
论文摘要
我们研究了配备了布朗运动的概率空间上反映的后退随机微分方程（RBSDE）。本文的主要新颖性实际上是，我们考虑到数据上的以下较弱的假设：障碍是（d）级的可选（满足弱的mokobodzki的状况），生成器是连续的，并且相对于可控制的（不可限制的增长），并且相对于可控的属性是可与可控的，并且是可与可控的情况下的，并且是可与端的序列和端的端子，并且是端的和端的端子。我们证明，在这些条件下，存在对相应RBSDE的解决方案。在本文的第二部分中，我们应用了RBSDE的理论来解决基于上述发电机的非线性期望驱动的Dynkin游戏中的基本问题。我们证明，RBSDE解决方案的主要组成部分代表相应的扩展非线性Dynkin游戏中的值过程。此外，我们为保证非线性Dynkin游戏的价值和鞍点的存在的障碍提供了足够的条件。
We study reflected backward stochastic differential equation (RBSDEs) on the probability space equipped with a Brownian motion. The main novelty of the paper lies in 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 restriction 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 condition on the barriers guaranteeing the existence of the value for nonlinear Dynkin games and the existence of a saddle point.
