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