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BSDEs with two reflecting barriers driven by a Brownian and a Poisson noise and related Dynkin game. (English) Zbl 1184.91038

Summary: In this paper we study BSDEs with two reflecting barriers driven by a Brownian motion and an independent Poisson process. We show the existence and uniqueness of local and global solutions. As an application we solve the related zero-sum Dynkin game.

MSC:

91A15 Stochastic games, stochastic differential games
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91A60 Probabilistic games; gambling
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