Date
2015
Dewey
Probabilités et mathématiques appliquées
Sujet
Second order backward stochastic differential equation; backward stochastic differential equation with jumps; model uncertainty; PIDEs; viscosity solutions.
Journal issue
Electronic Journal of Probability
Volume
20
Number
65
Publication date
2015
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
Author
Kazi-Tani, Mohamed Nabil
Possamaï, Dylan
Zhou, Chao
Type
Article accepté pour publication ou publié
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.
