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

Hamadène, Saïd; Hassani, Mohammed

Electron. J. Probab. 11, Paper No. 5, 121-145 (2006).

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

Keywords:

Backward stochastic differential equation; Poisson measure; Dynkin game; Mokobodzki’s condition