On the Malliavin differentiability of BSDEs

Thibaut Mastrolia (1, 2) , Dylan Possamaï (1) , Anthony Réveillac (3, 4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL
3 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse
4 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper we provide new conditions for the Malliavin differentiability of solutions of Lipschitz or quadratic BSDEs. Our results rely on the interpretation of the Malliavin derivative as a Gâteaux derivative in the directions of the Cameron-Martin space. Incidentally , we provide a new formulation for the characterization of the Malliavin-Sobolev type spaces $D^{1,p}$ .

Mots clés: BSDEs; abstract Wiener space; Malliavin's calculus

Domaines: Probabilités [math.PR]

Thibaut Mastrolia, Dylan Possamaï, Anthony Réveillac. On the Malliavin differentiability of BSDEs. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2016, ⟨10.1214/15-AIHP723⟩. ⟨hal-00971728v2⟩