On the uniqueness of solutions to quadratic BSDEs with non-convex generators

Philippe Briand (1) , Adrien Richou (2)

1 LAMA - Laboratoire de Mathématiques
2 IMB - Institut de Mathématiques de Bordeaux

In this paper we prove some uniqueness results for quadratic backward stochastic differential equations without any convexity assumptions on the generator. The bounded case is revisited while some new results are obtained in the unbounded case when the terminal condition and the generator depend on the path of a forward stochastic differential equation. Some of these results are based on strong estimates on Z that are interesting on their own and could be applied in other situations.

Mots clés: Backward stochastic differential equations; generator of quadratic growth; unbounded terminal condition; uniqueness result

Domaines: Probabilités [math.PR]

Philippe Briand, Adrien Richou. On the uniqueness of solutions to quadratic BSDEs with non-convex generators. Frontiers in stochastic analysis - BSDEs, SPDEs and their applications, 289, Springer, pp.89--107, 2019, Springer Proc. Math. Stat., ⟨10.1007/978-3-030-22285-7_3⟩. ⟨hal-01673587⟩