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Probability Theory and Related Fields 141, 3-4 (2008) 543-567

Quadratic BSDEs with convex generators and unbounded terminal conditions

Philippe Briand 1, 2, Ying Hu 1

(2008)

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.

1 :	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II
2 :	Laboratoire de Mathématiques (LAMA)
	CNRS : UMR5127 – Université de Savoie

Équipe de recherche : Processus stochastiques

Domaine

:

Mathématiques/Probabilités

Mots Clés : BSDEs – quadratic – convexity – uniqueness – unbounded terminal condition

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Contributeur : Philippe Briand <>

Soumis le : Mercredi 14 Mars 2007, 16:03:13

Dernière modification le : Jeudi 18 Mars 2010, 15:19:45