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

Freddy Delbaen (1) , Ying Hu (2) , Adrien Richou (3, 4)

1 Department of Mathematics - Department of Mathematics
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 IMB - Institut de Mathématiques de Bordeaux
4 ALEA - Advanced Learning Evolutionary Algorithms

In [3], the authors proved that uniqueness holds among solutions whose exponentials are $L^p$ with $p$ bigger than a constant $\gamma$ ($p>\gamma$). In this paper, we consider the critical case: $p=\gamma$. We prove that the uniqueness holds among solutions whose exponentials are $L^\gamma$ under the additional assumption that the generator is strongly convex.

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: the critical case. 2013. ⟨hal-00802330v1⟩