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

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  • M. Nabil Kazi-Tani
  • Dylan Possama\"i
  • 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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    File URL: http://arxiv.org/pdf/1208.0763
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1208.0763.

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    Date of creation: Aug 2012
    Date of revision: May 2014
    Handle: RePEc:arx:papers:1208.0763

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    Web page: http://arxiv.org/

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    1. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
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    Cited by:
    1. Dylan Possama\"i & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.

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