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. © Institute of Mathematical Statistics, 2013.
CITATION STYLE
Matoussi, A., Possamai, D., & Zhou, C. (2013). Second order reflected backward stochastic differential equations. Annals of Applied Probability, 23(6), 2420–2457. https://doi.org/10.1214/12-AAP906
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