Second Order BSDEs with Jumps, Part II: Existence and Applications
AbstractIn this paper, we follow the study of second order BSDEs with jumps started in our accompanying paper . We prove existence of these equations by a direct method, thus providing complete wellposedness for second order BSDEs. These equations are the natural candidates for the probabilistic interpretation of fully non-linear partial integro-differential equations, which is the point of our paper . Finally, we give an application of second order BSDEs to the study of a robust exponential utility maximization problem under model uncertainty. The uncertainty affects both the volatility process and the jump measure compensator. We prove existence of an optimal strategy, and that the value function of the problem is the unique solution of a particular second order BSDE with jumps.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1208.0763.
Date of creation: Aug 2012
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Web page: http://arxiv.org/
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- Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
- Dylan Possama\"i & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.
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