Nonlinear BSDEs with Two Optional Doob’s Class Barriers Satisfying Weak Mokobodzki’s Condition and Extended Dynkin Games

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