The Annals of Probability

Backward stochastic differential equations with reflection and Dynkin games

Jakša Cvitaniç and Ioannis Karatzas

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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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Ann. Probab. Volume 24, Number 4 (1996), 2024-2056.

First available in Project Euclid: 6 January 2003

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Zentralblatt MATH identifier

Primary: 93E05 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Backward SDE's reflecting barriers Dynkin games optimal stopping


Cvitaniç, Jakša; Karatzas, Ioannis. Backward stochastic differential equations with reflection and Dynkin games. Ann. Probab. 24 (1996), no. 4, 2024--2056. doi:10.1214/aop/1041903216.

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