Dynamic programming for a Markov-switching jump–diffusion
Autor(a) principal: | |
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Data de Publicação: | 2014 |
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/10400.22/5367 |
Resumo: | We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities. |
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Dynamic programming for a Markov-switching jump–diffusionStochastic optimal controlJump–diffusionMarkov-switchingOptimal consumption–investmentWe consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.ElsevierRepositório Científico do Instituto Politécnico do PortoAzevedo, NunoPinheiro, D.Weber, G.-W.2015-01-09T10:08:46Z20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/5367engIn "Journal of Computational and Applied Mathematics". ISSN 0377-0427. 267 (2014) 1-190377-042710.1016/j.cam.2014.01.021info: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:RCAAP2023-03-13T12:45:27Zoai:recipp.ipp.pt:10400.22/5367Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:26:02.829502Repositório 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 |
Dynamic programming for a Markov-switching jump–diffusion |
title |
Dynamic programming for a Markov-switching jump–diffusion |
spellingShingle |
Dynamic programming for a Markov-switching jump–diffusion Azevedo, Nuno Stochastic optimal control Jump–diffusion Markov-switching Optimal consumption–investment |
title_short |
Dynamic programming for a Markov-switching jump–diffusion |
title_full |
Dynamic programming for a Markov-switching jump–diffusion |
title_fullStr |
Dynamic programming for a Markov-switching jump–diffusion |
title_full_unstemmed |
Dynamic programming for a Markov-switching jump–diffusion |
title_sort |
Dynamic programming for a Markov-switching jump–diffusion |
author |
Azevedo, Nuno |
author_facet |
Azevedo, Nuno Pinheiro, D. Weber, G.-W. |
author_role |
author |
author2 |
Pinheiro, D. Weber, G.-W. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico do Porto |
dc.contributor.author.fl_str_mv |
Azevedo, Nuno Pinheiro, D. Weber, G.-W. |
dc.subject.por.fl_str_mv |
Stochastic optimal control Jump–diffusion Markov-switching Optimal consumption–investment |
topic |
Stochastic optimal control Jump–diffusion Markov-switching Optimal consumption–investment |
description |
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014 2014-01-01T00:00:00Z 2015-01-09T10:08:46Z |
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/10400.22/5367 |
url |
http://hdl.handle.net/10400.22/5367 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
In "Journal of Computational and Applied Mathematics". ISSN 0377-0427. 267 (2014) 1-19 0377-0427 10.1016/j.cam.2014.01.021 |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1799131354731905024 |