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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X04401168 |
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| _version_ | 1849401533240705024 |
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| author | Omid. S. Fard Ali V. Kamyad |
| author_facet | Omid. S. Fard Ali V. Kamyad |
| author_sort | Omid. S. Fard |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-8cc6cb45c4cd4993927e10e22e6212ee |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8cc6cb45c4cd4993927e10e22e6212ee2025-08-20T03:37:44ZengWileyJournal 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 |
| spellingShingle | Omid. S. Fard Ali V. Kamyad A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients Journal of Applied Mathematics |
| title | 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_short | A linear numerical scheme for nonlinear BSDEs with uniformly
continuous coefficients |
| title_sort | linear numerical scheme for nonlinear bsdes with uniformly continuous coefficients |
| url | http://dx.doi.org/10.1155/S1110757X04401168 |
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