Work

Second order reflected backward stochastic differential equations

Year: 2013

Type: article

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 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.

Source: The Annals of Applied Probability

DOI: 10.1214/12-aap906

Authors: Anis Matoussi, Dylan Possamai, Chao Zhou

Institutions: École Polytechnique, Le Mans Université, Université Paris Dauphine-PSL, Centre de Mathématiques Appliquées de l'École polytechnique

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: Fondation du Risque

OpenAlex ID: W2103530991