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BSDEs with jumps, optimization and applications to dynamic risk measures

Marie-Claire Quenez 1, 2 Agnès Sulem 2
2 MATHRISK - Mathematical Risk handling
Inria Paris-Rocquencourt, UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech
Abstract : In the Brownian case, the links between dynamic risk measures and BSDEs have been widely studied. In this paper, we study the case with jumps. We first study the properties of BSDEs driven by a Brownian motion and a Poisson random measure. In particular, we provide a comparison theorem, under quite weak assumptions, extending that of Royer \cite{R}. We then give some properties of dynamic risk measures induced by BSDEs with jumps. We provide a representation property of such dynamic risk measures in the convex case as well as some new results on a robust optimization problem, related to the case of model ambiguity
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https://hal.inria.fr/hal-00709632
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Marie-Claire Quenez, Agnès Sulem. BSDEs with jumps, optimization and applications to dynamic risk measures. Stochastic Processes and their Applications, Elsevier, 2013, 123 (8), pp.3328-3357. ⟨10.1016/j.spa.2013.02.016⟩. ⟨hal-00709632⟩

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