A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients

A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients

We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward stochastic differential equation (BSDE) and we get a...

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Main Authors: Omid. S. Fard, Ali V. Kamyad
Format: Article
Language:English
Published: Hindawi Limited 2004-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/S1110757X04401168
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spelling doaj-8cc6cb45c4cd4993927e10e22e6212ee2020-11-24T22:54:14ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422004-01-012004646147710.1155/S1110757X04401168A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficientsOmid. S. Fard0Ali V. Kamyad1Department of Mathematics, Damghan University of Basic Sciences, Damghan, IranDepartment of Mathematics, Ferdowsi University of Mashhad, Mashhad, IranWe attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE corresponding to the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original nonlinear BSDE.http://dx.doi.org/10.1155/S1110757X04401168
collection DOAJ
language English
format Article
sources DOAJ
author Omid. S. Fard
Ali V. Kamyad
spellingShingle Omid. S. Fard
Ali V. Kamyad
A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
Journal of Applied Mathematics
author_facet Omid. S. Fard
Ali V. Kamyad
author_sort Omid. S. Fard
title A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
title_short A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
title_full A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
title_fullStr A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
title_full_unstemmed A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
title_sort linear numerical scheme for nonlinear bsdes with uniformly continuous coefficients
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2004-01-01
description We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE corresponding to the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original nonlinear BSDE.
url http://dx.doi.org/10.1155/S1110757X04401168
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AT alivkamyad alinearnumericalschemefornonlinearbsdeswithuniformlycontinuouscoefficients
AT omidsfard linearnumericalschemefornonlinearbsdeswithuniformlycontinuouscoefficients
AT alivkamyad linearnumericalschemefornonlinearbsdeswithuniformlycontinuouscoefficients
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