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October 2008 Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison
Stéphane Crépey, Anis Matoussi
Ann. Appl. Probab. 18(5): 2041-2069 (October 2008). DOI: 10.1214/08-AAP517

Abstract

It is now established that under quite general circumstances, including in models with jumps, the existence of a solution to a reflected BSDE is guaranteed under mild conditions, whereas the existence of a solution to a doubly reflected BSDE is essentially equivalent to the so-called Mokobodski condition. As for uniqueness of solutions, this holds under mild integrability conditions. However, for practical purposes, existence and uniqueness are not enough. In order to further develop these results in Markovian set-ups, one also needs a (simply or doubly) reflected BSDE to be well posed, in the sense that the solution satisfies suitable bound and error estimates, and one further needs a suitable comparison theorem. In this paper, we derive such estimates and comparison results. In the last section, applicability of the results is illustrated with a pricing problem in finance.

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Stéphane Crépey. Anis Matoussi. "Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison." Ann. Appl. Probab. 18 (5) 2041 - 2069, October 2008. https://doi.org/10.1214/08-AAP517

Information

Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1158.60021
MathSciNet: MR2462558
Digital Object Identifier: 10.1214/08-AAP517

Subjects:
Primary: 60G40, 60G57, 60H10, 91B28

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 5 • October 2008
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