Doubly Reflected BSDEs with Integrable Parameters and Related Dynkin Games

Abstract: We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle L and the upper obstacle U of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by pasting local solutions, and show that the Y-component of the unique solution represents the value process of the corresponding Dynkin game under g-evaluation, a nonlinear expectation induced by BSDEs with the same generator g as the doubly reflected BSDE concerned. In particular, the first time  when process Y meets L and the first time  when process Y meets U form a saddle point of the Dynkin game.