The Annals of Probability

Backward stochastic differential equations with reflection and Dynkin games

Jakša Cvitaniç and Ioannis Karatzas

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 January 2003

Permanent link to this document
http://projecteuclid.org/euclid.aop/1041903216

Mathematical Reviews number (MathSciNet)
MR1415239

Digital Object Identifier
doi:10.1214/aop/1041903216

Zentralblatt MATH identifier
0876.60031

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

Keywords
Backward SDE's reflecting barriers Dynkin games optimal stopping

Citation

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. http://projecteuclid.org/euclid.aop/1041903216.


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