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On the Malliavin differentiability of BSDEs

Mastrolia, Thibaut; Possamaï, Dylan; Réveillac, Anthony (2017), On the Malliavin differentiability of BSDEs, Annales de l'I.H.P. Probabilités et Statistiques, 53, 1, p. 464-492. 10.1214/15-AIHP723

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1404.1026v4
Date
2017
Journal name
Annales de l'I.H.P. Probabilités et Statistiques
Volume
53
Number
1
Publisher
Gauthier-Villars
Published in
Paris
Pages
464-492
Publication identifier
Metadata
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Author(s)
Mastrolia, Thibaut
Possamaï, Dylan
Réveillac, Anthony
Abstract (EN)
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 $\mathbb D^{1,p}$.
Subjects / Keywords
Stochastic differential equations