Second order reflected backward stochastic differential equations
Zhou, Chao; Possamaï, Dylan; Matoussi, Anis (2013), Second order reflected backward stochastic differential equations, The Annals of Applied Probability, 23, 6, p. 2420-2457. http://dx.doi.org/10.1214/12-AAP906
TypeArticle accepté pour publication ou publié
Journal nameThe Annals of Applied Probability
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Abstract (EN)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.
Subjects / Keywordsreflected backward stochastic differential equation; Optimal stopping (Mathematical statistics); Lipschitz spaces; Stochastic differential equations; Hedging (Finance)
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Corrigendum for Second-order reflected backward stochastic differential equations" and "Second-order BSDEs with general reflection and game options under uncertainty" Matoussi, Anis; Possamaï, Dylan; Zhou, Chao (2017) Document de travail / Working paper