Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/27641 |
Resumo: | In many cases, financial option pricing models give rise to PDEs which turn out to be very difficult to solve by classical analytic tools. In this article, we study the numerical approximation in space of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with time and space-dependent coefficients. Making use of the L 2 theory of solvability in Sobolev spaces, the solution of the PDE problem is approximated in space, with finite-difference methods. The rate of convergence is estimated. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematicsFinancial Option PricingFinite-difference MethodsCauchy ProblemParabolic PartialDifferential EquationsMulti-dimensional EquationsIn many cases, financial option pricing models give rise to PDEs which turn out to be very difficult to solve by classical analytic tools. In this article, we study the numerical approximation in space of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with time and space-dependent coefficients. Making use of the L 2 theory of solvability in Sobolev spaces, the solution of the PDE problem is approximated in space, with finite-difference methods. The rate of convergence is estimated.EUDMC - The European Digital Mathematics LibraryRepositório da Universidade de LisboaGonçalves, Fernando F.Grossinho, Maria do Rosário2023-04-17T15:18:40Z20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/27641engGonçalves, Fernando F. and Maria do Rosário Grossinho .(2009). “Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics”. M a t h e m a t i c a B a l k a n i c a, New Series Vol. 23: Fasc. 1-2: pp. 111- 1320205 - 3217info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-04-23T01:30:51Zoai:www.repository.utl.pt:10400.5/27641Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:50:08.898415Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics |
title |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics |
spellingShingle |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics Gonçalves, Fernando F. Financial Option Pricing Finite-difference Methods Cauchy Problem Parabolic Partial Differential Equations Multi-dimensional Equations |
title_short |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics |
title_full |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics |
title_fullStr |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics |
title_full_unstemmed |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics |
title_sort |
Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics |
author |
Gonçalves, Fernando F. |
author_facet |
Gonçalves, Fernando F. Grossinho, Maria do Rosário |
author_role |
author |
author2 |
Grossinho, Maria do Rosário |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Gonçalves, Fernando F. Grossinho, Maria do Rosário |
dc.subject.por.fl_str_mv |
Financial Option Pricing Finite-difference Methods Cauchy Problem Parabolic Partial Differential Equations Multi-dimensional Equations |
topic |
Financial Option Pricing Finite-difference Methods Cauchy Problem Parabolic Partial Differential Equations Multi-dimensional Equations |
description |
In many cases, financial option pricing models give rise to PDEs which turn out to be very difficult to solve by classical analytic tools. In this article, we study the numerical approximation in space of the solution of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with time and space-dependent coefficients. Making use of the L 2 theory of solvability in Sobolev spaces, the solution of the PDE problem is approximated in space, with finite-difference methods. The rate of convergence is estimated. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009 2009-01-01T00:00:00Z 2023-04-17T15:18:40Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.5/27641 |
url |
http://hdl.handle.net/10400.5/27641 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Gonçalves, Fernando F. and Maria do Rosário Grossinho .(2009). “Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics”. M a t h e m a t i c a B a l k a n i c a, New Series Vol. 23: Fasc. 1-2: pp. 111- 132 0205 - 3217 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
EUDMC - The European Digital Mathematics Library |
publisher.none.fl_str_mv |
EUDMC - The European Digital Mathematics Library |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799131581148823552 |