On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions

Freddy Delbaen (1) , Ying Hu (2) , Adrien Richou (2)

1 Department of Mathematics - Department of Mathematics
2 IRMAR - Institut de Recherche Mathématique de Rennes

In a previous work, P. Briand and Y. Hu proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved by P. Briand and Y. Hu.

Mots clés: Backward stochastic differential equations; Generator of quadratic growth; Unbounded terminal condition; Uniqueness result; Nonlinear Feynman-Kac formula

Domaines: Probabilités [math.PR]

Freddy Delbaen, Ying Hu, Adrien Richou. On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2011, 47 (2), pp.559-574. ⟨10.1214/10-AIHP372⟩. ⟨hal-00391112⟩