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arXiv · 1403.2730

Quadratic BSDEs with jumps: related non-linear expectations

M. Nabil Kazi-Tani·Dylan Possamaï·Chao Zhou
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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

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M. Nabil Kazi-Tani, Dylan Possamaï, Chao Zhou. 2014-03-06. Quadratic BSDEs with jumps: related non-linear expectations. https://arxiv.org/abs/1403.2730

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