Quadratic BSDEs with convex generators and unbounded terminal conditions

Details Quadratic BSDEs with convex generators and unbounded terminal conditions Quadratic BSDEs with convex generators and unbounded terminal conditions

2007-03-14

arxiv.org/abs/math/0703423v1

Mathematics

Probability

Scientific paper

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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