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Quadratic BSDEs with jumps: a fixed-point approach

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  • M. Nabil Kazi-Tani
  • Dylan Possamai
  • Chao Zhou

Abstract

In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z,u). From a technical point of view, we use a direct fixed point approach as in Tevzadze [38], which allows us to obtain existence and uniqueness of a solution when the terminal condition is small enough. Then, thanks to a well-chosen splitting, we recover an existence result for general bounded solution. Under additional assumptions, we can obtain stability results and a comparison theorem, which as usual implies uniqueness.

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  • M. Nabil Kazi-Tani & Dylan Possamai & Chao Zhou, 2012. "Quadratic BSDEs with jumps: a fixed-point approach," Papers 1208.5581, arXiv.org, revised Mar 2014.
    • Handle: RePEc:arx:papers:1208.5581
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    References listed on IDEAS

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    1. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
    2. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
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