Publicação
Local dynamics for spherical optimal control problems
| Resumo: | In this paper we present results on the characterization of the local dynamics for infinite horizon discounted continuous time spherical optimal control problem. Though the dimension of the problem is almost overwhelming, the structure of the jacobian of the variational system allow us to make a complete characterization only by computing the sums of the principal minors of orders two, four and six. Using function of these minors, which are coefficients of a cubic reduced characteristic polynomial, we present a complete taxonomy for local dynamics. By using geometrical methods, we found that the maximum dimension of the stable manifold is three and that several kinds of bifurcations can occur: fold, Hopf, double-fold and fold-Hopf. A model for a representative consumer with habit formation and endogenous rate of time preference by Shi and Epstein (1993) was used both as an application and as a mean to compare with alternative methods of characterization of local dynamics. Differently from those authors we were able to prove the possibility of existence of an Hopf bifurcation for low levels of the coefficient of risk aversion and of the rate of habit formation. |
|---|---|
| Autores principais: | Brito, Paulo |
| Assunto: | Spherical Optimal Control Problems Local Dynamics Fold and Hopf Bifurcations Habit Formation Endogenous Time Preference |
| Ano: | 1996 |
| País: | Portugal |
| Tipo de documento: | working paper |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866810022430769152 |
|---|---|
| author | Brito, Paulo |
| author_facet | Brito, Paulo |
| author_role | author |
| contributor_name_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Brito, Paulo\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Brito, Paulo |
| datacite.date.Accepted.fl_str_mv | 1996-07-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2024-04-02T13:59:14Z |
| datacite.date.embargoed.fl_str_mv | 2024-04-02T13:59:14Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Spherical Optimal Control Problems Local Dynamics Fold and Hopf Bifurcations Habit Formation Endogenous Time Preference |
| datacite.titles.title.fl_str_mv | Local dynamics for spherical optimal control problems |
| dc.contributor.none.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Brito, Paulo |
| dc.date.Accepted.fl_str_mv | 1996-07-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2024-04-02T13:59:14Z |
| dc.date.embargoed.fl_str_mv | 2024-04-02T13:59:14Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10400.5/30512 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Banco de Portugal | Estudos e Documentos de Trabalho |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Spherical Optimal Control Problems Local Dynamics Fold and Hopf Bifurcations Habit Formation Endogenous Time Preference |
| dc.title.fl_str_mv | Local dynamics for spherical optimal control problems |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_8042 |
| description | In this paper we present results on the characterization of the local dynamics for infinite horizon discounted continuous time spherical optimal control problem. Though the dimension of the problem is almost overwhelming, the structure of the jacobian of the variational system allow us to make a complete characterization only by computing the sums of the principal minors of orders two, four and six. Using function of these minors, which are coefficients of a cubic reduced characteristic polynomial, we present a complete taxonomy for local dynamics. By using geometrical methods, we found that the maximum dimension of the stable manifold is three and that several kinds of bifurcations can occur: fold, Hopf, double-fold and fold-Hopf. A model for a representative consumer with habit formation and endogenous rate of time preference by Shi and Epstein (1993) was used both as an application and as a mean to compare with alternative methods of characterization of local dynamics. Differently from those authors we were able to prove the possibility of existence of an Hopf bifurcation for low levels of the coefficient of risk aversion and of the rate of habit formation. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | workingPaper |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/e6baf65d-c175-4651-a878-14483e822489/download |
| id | ul_7ade8317a32aaf82c06bc00c93b0607a |
| identifier.url.fl_str_mv | http://hdl.handle.net/10400.5/30512 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
| network_acronym_str | ul |
| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10400.5/30512 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Brito, Paulo |
| publishDate | 1996 |
| publisher.none.fl_str_mv | Banco de Portugal | Estudos e Documentos de Trabalho |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
| service_str_mv | urn:repositoryAcronym:ul |
| spelling | engBanco de Portugal | Estudos e Documentos de Trabalhopt_PTIn this paper we present results on the characterization of the local dynamics for infinite horizon discounted continuous time spherical optimal control problem. Though the dimension of the problem is almost overwhelming, the structure of the jacobian of the variational system allow us to make a complete characterization only by computing the sums of the principal minors of orders two, four and six. Using function of these minors, which are coefficients of a cubic reduced characteristic polynomial, we present a complete taxonomy for local dynamics. By using geometrical methods, we found that the maximum dimension of the stable manifold is three and that several kinds of bifurcations can occur: fold, Hopf, double-fold and fold-Hopf. A model for a representative consumer with habit formation and endogenous rate of time preference by Shi and Epstein (1993) was used both as an application and as a mean to compare with alternative methods of characterization of local dynamics. Differently from those authors we were able to prove the possibility of existence of an Hopf bifurcation for low levels of the coefficient of risk aversion and of the rate of habit formation.application/pdfpt_PTLocal dynamics for spherical optimal control problemsBrito, PauloHostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.ptISSNIsPartOf0870-01172024-04-02T13:59:14Z1996-071996-07-01T00:00:00ZHandlehttp://hdl.handle.net/10400.5/30512http://purl.org/coar/access_right/c_abf2open accessSpherical Optimal Control ProblemsLocal DynamicsFold and Hopf BifurcationsHabit FormationEndogenous Time Preference1303698 bytesother research producthttp://purl.org/coar/resource_type/c_8042working paperhttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/e6baf65d-c175-4651-a878-14483e822489/download |
| spellingShingle | Local dynamics for spherical optimal control problems Brito, Paulo Spherical Optimal Control Problems Local Dynamics Fold and Hopf Bifurcations Habit Formation Endogenous Time Preference |
| status | SINGLETON |
| subject.fl_str_mv | Spherical Optimal Control Problems Local Dynamics Fold and Hopf Bifurcations Habit Formation Endogenous Time Preference |
| title | Local dynamics for spherical optimal control problems |
| title_full | Local dynamics for spherical optimal control problems |
| title_fullStr | Local dynamics for spherical optimal control problems |
| title_full_unstemmed | Local dynamics for spherical optimal control problems |
| title_short | Local dynamics for spherical optimal control problems |
| title_sort | Local dynamics for spherical optimal control problems |
| topic | Spherical Optimal Control Problems Local Dynamics Fold and Hopf Bifurcations Habit Formation Endogenous Time Preference |
| topic_facet | Spherical Optimal Control Problems Local Dynamics Fold and Hopf Bifurcations Habit Formation Endogenous Time Preference |
| url | http://hdl.handle.net/10400.5/30512 |
| visible | 1 |