Dynamic programming for a Markov-switching jump–diffusion

Detalhes bibliográficos
Autor(a) principal: Azevedo, Nuno
Data de Publicação: 2014
Outros Autores: Pinheiro, D., Weber, G.-W.
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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spelling 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
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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
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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)
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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