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arXiv · 1208.0763

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

M. Nabil Kazi-Tani·Dylan Possamaï·Chao Zhou
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Abstract

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.

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BibTeXRIS

M. Nabil Kazi-Tani, Dylan Possamaï, Chao Zhou. 2014-05-27. Second Order BSDEs with Jumps: Existence and probabilistic representation for fully-nonlinear PIDEs. https://arxiv.org/abs/1208.0763

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