On the Malliavin differentiability of BSDEs
Thibaut Mastrolia, Dylan Possama\"i, Anthony R\'eveillac
TL;DR
This paper establishes new conditions under which solutions to Lipschitz and quadratic backward stochastic differential equations (BSDEs) are Malliavin differentiable, using a Gâteaux derivative approach in the Cameron-Martin space.
Contribution
It introduces novel criteria for Malliavin differentiability of BSDE solutions and offers a new formulation for Malliavin-Sobolev spaces D^{1,p}.
Findings
New conditions for Malliavin differentiability of BSDE solutions.
A Gâteaux derivative interpretation of the Malliavin derivative.
A reformulation of the characterization of D^{1,p} spaces.
Abstract
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 G{\^a}teaux derivative in the directions of the Cameron-Martin space. Incidentally, we provide a new formulation for the characterization of the Malliavin-Sobolev type spaces .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Nonlinear Partial Differential Equations · Navier-Stokes equation solutions