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arXiv · 1201.0746

Second order reflected backward stochastic differential equations

Anis Matoussi·Dylan Possamaï·Chao Zhou
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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.

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Anis Matoussi, Dylan Possamaï, Chao Zhou. 2012-01-03. Second order reflected backward stochastic differential equations. https://doi.org/10.1214/12-aap906

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