Quadratic BSDEs with jumps: related non-linear expectations
Abstract
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
Cite
@article{arxiv.1403.2730,
title = {Quadratic BSDEs with jumps: related non-linear expectations},
author = {M. Nabil Kazi-Tani and Dylan Possamaï and Chao Zhou},
journal= {arXiv preprint arXiv:1403.2730},
year = {2014}
}
Comments
28 pages. Formerly part of arXiv:1208.5581