Thumbnail

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

View/Open
Type
Article accepté pour publication ou publié
Date
2015
Journal name
Electronic Journal of Probability
Volume
20
Number
65
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
Publication identifier
Metadata
Show full item record
Author(s)
Kazi-Tani, Mohamed Nabil
Possamaï, Dylan
Zhou, Chao
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 / Keywords
Second order backward stochastic differential equation; backward stochastic differential equation with jumps; model uncertainty; PIDEs; viscosity solutions.