On the convergence of the Sakawa-Shindo algorithm in stochastic control

Autores
Bonnans, J. Frédéric; Gianatti, Justina; Silva, Francisco J.
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We analyze an algorithm for solving stochastic control problems, based on Pontryagin’s maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of the cost functions as well as, in the convex case, the fact that the sequence of controls is minimizing, and converges to an optimal solution if it is bounded. In a specific case we interpret the algorithm as the gradient plus projection method and obtain a linear convergence rate to the solution.
Fil: Bonnans, J. Frédéric. Ecole Polytechnique and Laboratoire de Finance des Marchés d'Énergie. Centre de Mathématiques Appliquées; Francia. Institut National de Recherche en Informatique et en Automatique; Francia
Fil: Gianatti, Justina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Silva, Francisco J.. Université de Limoges. Faculté des sciences et techniques; Francia. Centre National de la Recherche Scientifique; Francia
Materia
FIRST ORDER ALGORITHM
PONTRYAGIN'S PRINCIPLE
STOCHASTIC CONTROL
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/50342
Acceder
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spelling On the convergence of the Sakawa-Shindo algorithm in stochastic controlBonnans, J. FrédéricGianatti, JustinaSilva, Francisco J.FIRST ORDER ALGORITHMPONTRYAGIN'S PRINCIPLESTOCHASTIC CONTROLhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We analyze an algorithm for solving stochastic control problems, based on Pontryagin’s maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of the cost functions as well as, in the convex case, the fact that the sequence of controls is minimizing, and converges to an optimal solution if it is bounded. In a specific case we interpret the algorithm as the gradient plus projection method and obtain a linear convergence rate to the solution.Fil: Bonnans, J. Frédéric. Ecole Polytechnique and Laboratoire de Finance des Marchés d'Énergie. Centre de Mathématiques Appliquées; Francia. Institut National de Recherche en Informatique et en Automatique; FranciaFil: Gianatti, Justina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; ArgentinaFil: Silva, Francisco J.. Université de Limoges. Faculté des sciences et techniques; Francia. Centre National de la Recherche Scientifique; FranciaAmerican Institute of Mathematical Sciences2016-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/50342Bonnans, J. Frédéric; Gianatti, Justina; Silva, Francisco J.; On the convergence of the Sakawa-Shindo algorithm in stochastic control; American Institute of Mathematical Sciences; Mathematical Control and Related Fields; 6; 3; 9-2016; 391-4062156-84722156-8499CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3934/mcrf.2016008info:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12756info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:09Zoai:ri.conicet.gov.ar:11336/50342instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:50:09.467CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the convergence of the Sakawa-Shindo algorithm in stochastic control
title On the convergence of the Sakawa-Shindo algorithm in stochastic control
spellingShingle On the convergence of the Sakawa-Shindo algorithm in stochastic control
Bonnans, J. Frédéric
FIRST ORDER ALGORITHM
PONTRYAGIN'S PRINCIPLE
STOCHASTIC CONTROL
title_short On the convergence of the Sakawa-Shindo algorithm in stochastic control
title_full On the convergence of the Sakawa-Shindo algorithm in stochastic control
title_fullStr On the convergence of the Sakawa-Shindo algorithm in stochastic control
title_full_unstemmed On the convergence of the Sakawa-Shindo algorithm in stochastic control
title_sort On the convergence of the Sakawa-Shindo algorithm in stochastic control
dc.creator.none.fl_str_mv Bonnans, J. Frédéric
Gianatti, Justina
Silva, Francisco J.
author Bonnans, J. Frédéric
author_facet Bonnans, J. Frédéric
Gianatti, Justina
Silva, Francisco J.
author_role author
author2 Gianatti, Justina
Silva, Francisco J.
author2_role author
author
dc.subject.none.fl_str_mv FIRST ORDER ALGORITHM
PONTRYAGIN'S PRINCIPLE
STOCHASTIC CONTROL
topic FIRST ORDER ALGORITHM
PONTRYAGIN'S PRINCIPLE
STOCHASTIC CONTROL
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We analyze an algorithm for solving stochastic control problems, based on Pontryagin’s maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of the cost functions as well as, in the convex case, the fact that the sequence of controls is minimizing, and converges to an optimal solution if it is bounded. In a specific case we interpret the algorithm as the gradient plus projection method and obtain a linear convergence rate to the solution.
Fil: Bonnans, J. Frédéric. Ecole Polytechnique and Laboratoire de Finance des Marchés d'Énergie. Centre de Mathématiques Appliquées; Francia. Institut National de Recherche en Informatique et en Automatique; Francia
Fil: Gianatti, Justina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentina
Fil: Silva, Francisco J.. Université de Limoges. Faculté des sciences et techniques; Francia. Centre National de la Recherche Scientifique; Francia
description We analyze an algorithm for solving stochastic control problems, based on Pontryagin’s maximum principle, due to Sakawa and Shindo in the deterministic case and extended to the stochastic setting by Mazliak. We assume that either the volatility is an affine function of the state, or the dynamics are linear. We obtain a monotone decrease of the cost functions as well as, in the convex case, the fact that the sequence of controls is minimizing, and converges to an optimal solution if it is bounded. In a specific case we interpret the algorithm as the gradient plus projection method and obtain a linear convergence rate to the solution.
publishDate 2016
dc.date.none.fl_str_mv 2016-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/50342
Bonnans, J. Frédéric; Gianatti, Justina; Silva, Francisco J.; On the convergence of the Sakawa-Shindo algorithm in stochastic control; American Institute of Mathematical Sciences; Mathematical Control and Related Fields; 6; 3; 9-2016; 391-406
2156-8472
2156-8499
CONICET Digital
CONICET
url http://hdl.handle.net/11336/50342
identifier_str_mv Bonnans, J. Frédéric; Gianatti, Justina; Silva, Francisco J.; On the convergence of the Sakawa-Shindo algorithm in stochastic control; American Institute of Mathematical Sciences; Mathematical Control and Related Fields; 6; 3; 9-2016; 391-406
2156-8472
2156-8499
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3934/mcrf.2016008
info:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=12756
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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