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
MetadataShow full item record
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 (2021) Article accepté pour publication ou publié