BACKWARD STOCHASTIC DIFFERENTIAL-EQUATIONS WITH REFLECTION AND DYNKINGAMES

We establish existence and uniqueness results for adapted solutions of backward stochastic differential equations (BSDE's) with two reflecti ng barriers, generalizing the work of El Karoui, Kapoudjian, Pardoux, Peng and Quenez. Existence is proved first by solving a related pair o f coupled optimal stopping problems, and then, under different conditi ons, via a penalization method. It is also shown that the solution coi ncides with the value of a certain Dynkin game, a stochastic game of o ptimal stopping. Moreover, the connection with the backward SDE enable s us to provide a pathwise (deterministic) approach to the game.