Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs
Kazi-Tani, Mohamed Nabil; Possamaï, Dylan; Zhou, Chao (2015), Second order BSDEs with jumps: existence and probabilistic representation for fully-nonlinear PIDEs, Electronic Journal of Probability, 20, 65. 10.1214/EJP.v20-3569
TypeArticle accepté pour publication ou publié
Journal nameElectronic Journal of Probability
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Abstract (EN)In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in an accompanying paper. We prove existence of these equations by a direct method, thus providing complete wellposedness for 2BSDEJs. These equations are a natural candidate for the probabilistic interpretation of some fully non-linear partial integro-differential equations, which is the point of the second part of this work. We prove a non-linear Feynman-Kac formula and show that solutions to 2BSDEJs provide viscosity solutions of the associated PIDEs.
Subjects / KeywordsSecond order backward stochastic differential equation; backward stochastic differential equation with jumps; model uncertainty; PIDEs; viscosity solutions.
Showing items related by title and author.
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