Quadratic BSDEs with Jumps and Related Non-linear Expectations: a Fixed-point Approach
AbstractWe prove the existence of bounded solutions of quadratic backward SDEs with jumps, using a direct fixed point approach as in Tevzadze . Under an additional standard assumption, we prove a uniqueness result, thanks to a comparison theorem. Then we study the properties of the corresponding $g$-expectations, we obtain in particular a non linear Doob-Meyer decomposition for $g$-submartingales and their regularity in time. As a consequence of this results, we obtain a converse comparison theorem for our class of BSDEs. We give applications for dynamic risk measures and their dual representation, and compute their inf-convolution, with some explicit examples.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1208.5581.
Date of creation: Aug 2012
Date of revision: Oct 2012
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Web page: http://arxiv.org/
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