Second Order BSDEs with Jumps: Existence and probabilistic   representation for fully-nonlinear PIDEs
  In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJs for short) started in our accompanying paper [15]. 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. 
M. Nabil Kazi-Tani, Dylan Possama\"i, Chao Zhou
math.PR q-fin.PM q-fin.RM