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Quadratic BSDEs with convex generators and unbounded terminal conditions

Abstract : In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context.
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https://hal.archives-ouvertes.fr/hal-00136605
Contributor : Philippe Briand Connect in order to contact the contributor
Submitted on : Wednesday, March 14, 2007 - 4:03:13 PM
Last modification on : Wednesday, April 6, 2022 - 3:48:03 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 1:34:34 AM

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Philippe Briand, Ying Hu. Quadratic BSDEs with convex generators and unbounded terminal conditions. Probability Theory and Related Fields, Springer Verlag, 2008, 141 (3-4), pp.543-567. ⟨hal-00136605⟩

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