2012/01/31 by Anis Matoussi, Dylan Possamaï, Dylan Possamai +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #stochastic dynamics and bifurcation
paper · pdf · doi:10.1214/12-aap906
published as Annals of Applied Probability 2013, Vol. 23, No. 6, 2420-2457 · 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
openalex publication_date 2013/10/22 · arxiv created 2015/04/04 · arxiv updated 2015/04/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.