A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations

A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations

Abstract The purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteris...

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Main Authors: Xiaofei Li, Yi Wu, Quanxin Zhu, Songbo Hu, Chuan Qin
Format: Article
Language:English
Published: SpringerOpen 2021-04-01
Series:Advances in Difference Equations
Subjects:
Forward backward stochastic differential equations
Fourier cos-cos transform
Characteristic functions
Least-squares regressions
Monte Carlo
Online Access:https://doi.org/10.1186/s13662-021-03361-5
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spelling doaj-be60000cbcba4d36abd815ecb96019c92021-04-18T11:44:17ZengSpringerOpenAdvances in Difference Equations1687-18472021-04-012021111310.1186/s13662-021-03361-5A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equationsXiaofei Li0Yi Wu1Quanxin Zhu2Songbo Hu3Chuan Qin4Zhuhai Da Hengqin Science and Technology Development Co LtdSchool of Information and Mathematics, Yangtze UniversityMOE LCSM, School of Mathematics and Statistics, Hunan Normal UniversityJiangxi Province Key Laboratory of Preventive Medicine, School of Public Health, Nanchang UniversityCollege of Engineering and Technology, Yangtze UniversityAbstract The purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteristic functions. A new numerical scheme is proposed by using the least-squares regression-based Monte Carlo method to solve the initial value of FBSDEs. Finally, a numerical experiment in European option pricing is implemented to test the efficiency and stability of this scheme.https://doi.org/10.1186/s13662-021-03361-5Forward backward stochastic differential equationsFourier cos-cos transformCharacteristic functionsLeast-squares regressionsMonte Carlo
collection DOAJ
language English
format Article
sources DOAJ
author Xiaofei Li
Yi Wu
Quanxin Zhu
Songbo Hu
Chuan Qin
spellingShingle Xiaofei Li
Yi Wu
Quanxin Zhu
Songbo Hu
Chuan Qin
A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations
Advances in Difference Equations
Forward backward stochastic differential equations
Fourier cos-cos transform
Characteristic functions
Least-squares regressions
Monte Carlo
author_facet Xiaofei Li
Yi Wu
Quanxin Zhu
Songbo Hu
Chuan Qin
author_sort Xiaofei Li
title A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations
title_short A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations
title_full A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations
title_fullStr A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations
title_full_unstemmed A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations
title_sort regression-based monte carlo method to solve two-dimensional forward backward stochastic differential equations
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-04-01
description Abstract The purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteristic functions. A new numerical scheme is proposed by using the least-squares regression-based Monte Carlo method to solve the initial value of FBSDEs. Finally, a numerical experiment in European option pricing is implemented to test the efficiency and stability of this scheme.
topic Forward backward stochastic differential equations
Fourier cos-cos transform
Characteristic functions
Least-squares regressions
Monte Carlo
url https://doi.org/10.1186/s13662-021-03361-5
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