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In this paper, we pursue the study of second order BSDEs with jumps (2BSDEJsfor short) started in our accompanying paper [15]. We prove existence of theseequations by a direct method, thus providing complete wellposedness for2BSDEJs. These equations are a natural candidate for the probabilisticinterpretation of some fully non-linear partial integro-differential equations,which is the point of the second part of this work. We prove a non-linearFeynman-Kac formula and show that solutions to 2BSDEJs provide viscositysolutions of the associated PIDEs.

Second Order BSDEs with Jumps: Existence and probabilistic representation for fully-nonlinear PIDEs