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Article Dans Une Revue Stochastics and Dynamics Année : 2016

Quadratic BSDEs with jumps: Related nonlinear expectations

Résumé

In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z, u), started in our accompanying paper [15]. Relying on the existence and uniqueness result of [15], we define the corresponding g-expectations and study some of their properties. We obtain in particular a non-linear Doob-Meyer decomposition for g-submartingales and a downcrossing inequality which implies their regularity in time. As a consequence of these results, we also obtain a converse comparison theorem for our class of BSDEs. Finally, we provide a dual representation for the corresponding dynamic risk measures, and study the properties of their inf-convolution, giving several explicit examples.
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hal-01432974 , version 1 (12-01-2017)

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Mohamed Nabil Kazi-Tani, Dylan Possamaï, Chao Zhou. Quadratic BSDEs with jumps: Related nonlinear expectations. Stochastics and Dynamics, 2016, 16 (4), pp.1650012. ⟨10.1142/S021949371650012X⟩. ⟨hal-01432974⟩
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