Second order reflected backward stochastic differential equations
Abstract
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 c\`adl\`ag 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.
Keywords
Cite
@article{arxiv.1201.0746,
title = {Second order reflected backward stochastic differential equations},
author = {Anis Matoussi and Dylan Possamaï and Chao Zhou},
journal= {arXiv preprint arXiv:1201.0746},
year = {2015}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AAP906 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1003.6053 by other authors