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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 Possamai
  • Chao Zhou

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.

Suggested Citation

  • M. Nabil Kazi-Tani & Dylan Possamai & Chao Zhou, 2012. "Second Order BSDEs with Jumps: Existence and probabilistic representation for fully-nonlinear PIDEs," Papers 1208.0763, arXiv.org, revised May 2014.
    • Handle: RePEc:arx:papers:1208.0763
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    References listed on IDEAS

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    1. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    2. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
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    Cited by:

    1. Dylan Possamai & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.

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