We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b). Copyright Blackwell Publishers Inc. 1997.
International audienceIn 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 ambiguityLes liens entre les EDSR et les mesures de risque dynamiques ont été largement étudiées dans le cas Brownien. On étudie dans ce papier le cas avec sauts. On étudie tout d'abord les propriétés des EDSR dirigées par un mouvement Brownien et une mesure de Poisson aléatoire : on prouve en particulier un théoréme de comparaison sous des hypothéses assez faibles qui généralise celui de Royer 2006. On donne ensuite des propriétés pour les mesures de risques dynamiques induites par les EDSR avec sauts. On établit un théoréme de représentation duale pour de telles mesures de risques dans le cas convexe. On étudie enfin un probléme d'optimisation robuste de mesure de risques associé au cas d'ambiguité de modéle
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