SECOND ORDER REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Matoussi, Anis; Possamai, Dylan; Zhou, Chao
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Le Mans Universite; Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP906
• 发表日期: 2013
• 页码: 2420-2457
• 关键词: nonlinear expectations; bsde; part

摘要

In this article, we build upon the work of Soner, Touzi and Zhang [Probab. Theory Related Fields 153 (2012) 149-190] to define a notion of a second order backward stochastic differential equation reflected on a lower cadlag obstacle. We prove existence and uniqueness of the solution under a Lipschitz-type assumption on the generator, and we investigate some links between our reflected 2BSDEs and nonclassical optimal stopping problems. Finally, we show that reflected 2BSDEs provide a super-hedging price for American options in a market with volatility uncertainty.