Backward stochastic differential equations with reflection and Dynkin games. (English) Zbl 0876.60031

The authors study backward stochastic differential equations with reflection (RBSDE’s) on two stochastic barriers (upper and lower boundary processes) in relation both with Dynkin games and coupled optimal stopping problems. The uniqueness of the solution of an RBSDE is proved using that any such solution is the (unique) value of a Dynkin game. The existence of a solution of this RBSDE is proved using that a pair of coupled optimal stopping problems has a solution. The authors present also an alternative method to prove existence of a solution of the RBSDE using a more classical penalization method. In the last section the authors study a pathwise approach to the Dynkin game.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91A60 Probabilistic games; gambling
60G40 Stopping times; optimal stopping problems; gambling theory
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