Discretization and Machine Learning Approximation of BSDEs with a Constraint on the Gains-Process - Université d'Évry Access content directly
Preprints, Working Papers, ... Year : 2020

Discretization and Machine Learning Approximation of BSDEs with a Constraint on the Gains-Process

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. Mathematics Subject Classification (2010): 65C30, 65M75, 60H35, 93E20, 49L25.
Fichier principal
Vignette du fichier
ConstBSDENN.pdf (988.78 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02468354 , version 1 (05-02-2020)

Identifiers

Cite

Idris Kharroubi, Thomas Lim, Xavier Warin. Discretization and Machine Learning Approximation of BSDEs with a Constraint on the Gains-Process. 2020. ⟨hal-02468354⟩
82 View
98 Download

Altmetric

Share

Gmail Facebook X LinkedIn More