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
Pages (from-to)	183-203
Number of pages	21
Journal	Monte Carlo Methods and Applications
Volume	30
Issue number	2
Early online date	1 Feb 2024
DOIs	https://doi.org/10.1515/mcma-2024-2002
Publication status	Published - 1 Jun 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

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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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T1 - A gradient method for high-dimensional BSDEs

AU - Gnameho, Kossi

AU - Stadje, Mitja

AU - Pelsser, Antoon

N1 - data: no data used

PY - 2024/6/1

Y1 - 2024/6/1

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

VL - 30

SP - 183

EP - 203

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

IS - 2

ER -

A gradient method for high-dimensional BSDEs

Abstract

Keywords

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