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Quadratic BSDEs with jumps: related non-linear expectations

Kazi-Tani, Mohamed Nabil; Possamaï, Dylan; Zhou, Chao (2016), Quadratic BSDEs with jumps: related non-linear expectations, Stochastics and Dynamics, 16, 4, p. n°1650012. 10.1142/S021949371650012X

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1403.2730v1
Date
2016
Journal name
Stochastics and Dynamics
Volume
16
Number
4
Publisher
World Scientific
Published in
Paris
Pages
n°1650012
Publication identifier
Metadata
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Author(s)
Kazi-Tani, Mohamed Nabil
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Possamaï, Dylan
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Zhou, Chao
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.
Subjects / Keywords
dynamic risk measures; inf-convolution; BSDEs; on-linear Doob-Meyer decomposition; jumps; quadratic growth