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 càdlàg 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.

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

References in corpus (4)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• Martingale approach to stochastic differential games of control and stopping
• Pathwise Construction of Stochastic Integrals
• Skorohod Equation and Reflected Backward Stochastic Differential Equations

Cited by in corpus (3)

• Arbitrage and duality in nondominated discrete-time models
• Optimal stopping under adverse nonlinear expectation and related games
• A New Result for Second Order BSDEs with Quadratic Growth and its Applications