BSDEs with jumps, optimization and applications to dynamic risk measures

In the Brownian case, the links between dynamic risk measures and BSDEs have been widely studied. In this paper, we consider 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  [21]. 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 results on a robust optimization problem in the case of model ambiguity.