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Quadratic BSDEs with jumps: a fixed-point approach

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  • M. Nabil Kazi-Tani
  • Dylan Possama\"i
  • Chao Zhou
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    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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    File URL: http://arxiv.org/pdf/1208.5581
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    Paper provided by arXiv.org in its series Papers with number 1208.5581.

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    Date of creation: Aug 2012
    Date of revision: Mar 2014
    Handle: RePEc:arx:papers:1208.5581

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