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Quadratic BSDEs with jumps: related non-linear expectations

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Date
2016
Publisher city
Paris
Link to item file
https://arxiv.org/abs/1403.2730v1
Dewey
Probabilités et mathématiques appliquées
Sujet
dynamic risk measures; inf-convolution; BSDEs; on-linear Doob-Meyer decomposition; jumps; quadratic growth
Journal issue
Stochastics and Dynamics
Volume
16
Number
4
Publication date
2016
Article pages
n°1650012
Publisher
World Scientific
DOI
http://dx.doi.org/10.1142/S021949371650012X
URI
https://basepub.dauphine.fr/handle/123456789/12927
Collections
  • CEREMADE : Publications
Metadata
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Author
Kazi-Tani, Mohamed Nabil
89626 Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Possamaï, Dylan
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Zhou, Chao
Type
Article accepté pour publication ou publié
Abstract (EN)
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 un iqueness 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 downcrossinginequality 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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