Discretization and machine learning approximation of BSDEs with a constraint on the Gains-process

Kharroubi Idris (), Lim Thomas () and Warin Xavier ()
Additional contact information
Kharroubi Idris: Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistiques et Modélisations (LPSM), Paris, France
Lim Thomas: ENSIIE, Laboratoire de Mathématiques et Modélisation d’Evry, CNRS UMR 8071, Evry, France
Warin Xavier: EDF R&D and FiME, Paris, France

Monte Carlo Methods and Applications, 2021, vol. 27, issue 1, 27-55

Abstract: We study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments.

Keywords: Constrainted BSDEs; discrete-time approximation; neural networks approximation; facelift transformation (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2020-2080 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:27:y:2021:i:1:p:27-55:n:1

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/mcma-2020-2080

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().