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Article Dans Une Revue The Annals of Applied Probability Année : 2013

Second order reflected backward stochastic differential equations

Résumé

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\'{a}dl\'{a}g 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.

Dates et versions

hal-00919119 , version 1 (16-12-2013)

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Anis Matoussi, Dylan Possamaï, Chao Zhou. Second order reflected backward stochastic differential equations. The Annals of Applied Probability, 2013, 23 (6), pp.2420-2457. ⟨10.1214/12-AAP906⟩. ⟨hal-00919119⟩
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