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 on the Brownian filtration with two optional barriers of class (D) satisfying weak Mokobodzki's condition. We prove an existence and uniqueness result in case of integrable data. We also show a relation between the main component of a solution to RBSDE and the value process in corresponding extended nonlinear Dynkin game.