Numerical approximation of multidimensional parabolic partial differential equations arising in financial mathematics

Detalhes bibliográficos
Autor(a) principal: Gonçalves, Fernando F.
Data de Publicação: 2009
Outros Autores: Grossinho, Maria do Rosário
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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spelling 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
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