A gradient method for high-dimensional BSDEs

Kossi Gnameho; Mitja Stadje; Antoon Pelsser

doi:10.1515/mcma-2024-2002

A gradient method for high-dimensional BSDEs

Kossi Gnameho^*, Mitja Stadje, Antoon Pelsser

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions. The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients. We propose numerical experiments to illustrate its performance.

Original language	English
Number of pages	21
Journal	Monte Carlo Methods and Applications
DOIs	https://doi.org/10.1515/mcma-2024-2002
Publication status	E-pub ahead of print - 1 Feb 2024

Keywords

Regression
BSDE
Monte Carlo
Hermite polynomials
STOCHASTIC DIFFERENTIAL-EQUATIONS
MONTE-CARLO METHOD
NUMERICAL SCHEME
BACKWARD SDES
CONVERGENCE
SIMULATION
DISCRETIZATION
APPROXIMATION
EXPANSION

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10.1515/mcma-2024-2002Licence: CC BY

Cite this

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title = "A gradient method for high-dimensional BSDEs",

abstract = "We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions. The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients. We propose numerical experiments to illustrate its performance.",

keywords = "Regression, BSDE, Monte Carlo, Hermite polynomials, STOCHASTIC DIFFERENTIAL-EQUATIONS, MONTE-CARLO METHOD, NUMERICAL SCHEME, BACKWARD SDES, CONVERGENCE, SIMULATION, DISCRETIZATION, APPROXIMATION, EXPANSION",

author = "Kossi Gnameho and Mitja Stadje and Antoon Pelsser",

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AU - Stadje, Mitja

AU - Pelsser, Antoon

N1 - data:

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N2 - We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions. The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients. We propose numerical experiments to illustrate its performance.

AB - We develop a Monte Carlo method to solve backward stochastic differential equations (BSDEs) in high dimensions. The proposed algorithm is based on the regression-later approach using multivariate Hermite polynomials and their gradients. We propose numerical experiments to illustrate its performance.

KW - Regression

KW - BSDE

KW - Monte Carlo

KW - Hermite polynomials

KW - STOCHASTIC DIFFERENTIAL-EQUATIONS

KW - MONTE-CARLO METHOD

KW - NUMERICAL SCHEME

KW - BACKWARD SDES

KW - CONVERGENCE

KW - SIMULATION

KW - DISCRETIZATION

KW - APPROXIMATION

KW - EXPANSION

U2 - 10.1515/mcma-2024-2002

DO - 10.1515/mcma-2024-2002

M3 - Article

SN - 0929-9629

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

ER -