REFLECTED AND DOUBLY REFLECTED BSDES WITH JUMPS: A PRIORI ESTIMATES AND COMPARISON

• 成果类型: Article
• 署名作者: Crepey, Stephane; Matoussi, Anis
• 署名单位: Universite Paris Saclay; Le Mans Universite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP517
• 发表日期: 2008
• 页码: 2041-2069
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; backward sdes; barriers; systems; game

摘要

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.