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October 1996 Backward stochastic differential equations with reflection and Dynkin games
Jakša Cvitaniç, Ioannis Karatzas
Ann. Probab. 24(4): 2024-2056 (October 1996). DOI: 10.1214/aop/1041903216


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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Jakša Cvitaniç. Ioannis Karatzas. "Backward stochastic differential equations with reflection and Dynkin games." Ann. Probab. 24 (4) 2024 - 2056, October 1996.


Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0876.60031
MathSciNet: MR1415239
Digital Object Identifier: 10.1214/aop/1041903216

Primary: 60H10 , 93E05
Secondary: 60G40

Keywords: Backward SDE's , Dynkin games , Optimal stopping , reflecting barriers

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 4 • October 1996
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