Quadratic BSDEs with convex generators and unbounded terminal conditions

Philippe Briand (1, 2) , Ying Hu (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LAMA - Laboratoire de Mathématiques

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.

Mots clés: BSDEs; quadratic; convexity; uniqueness; unbounded terminal condition

Domaines: Probabilités [math.PR]

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