A class of ito diffusions with known terminal value and specified optimal barrier

In this paper, we study the optimal stopping-time problems related to a class of Ito diffusions, modeling for example an investment gain, for which the terminal value is a priori known. This could be the case of an insider trading or of the pinning at expiration of stock options. We give the explici...

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Detalhes bibliográficos
Autores: D'Auria, Bernardo, Ferriero, Alessandro
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/691253
Acesso em linha:http://hdl.handle.net/10486/691253
https://dx.doi.org/10.3390/math8010123
Access Level:acceso abierto
Palavra-chave:Brownian bridge
Hamilton-Jacobi-Bellman equation
Liquidation strategy
Optimal stopping time
Matemáticas
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spelling A class of ito diffusions with known terminal value and specified optimal barrierD'Auria, BernardoFerriero, AlessandroBrownian bridgeHamilton-Jacobi-Bellman equationLiquidation strategyOptimal stopping timeMatemáticasIn this paper, we study the optimal stopping-time problems related to a class of Ito diffusions, modeling for example an investment gain, for which the terminal value is a priori known. This could be the case of an insider trading or of the pinning at expiration of stock options. We give the explicit solution to these optimization problems and in particular we provide a class of processes whose optimal barrier has the same form as the one of the Brownian bridge. These processes may be a possible alternative to the Brownian bridge in practice as they could better model real applications. Moreover, we discuss the existence of a process with a prescribed curve as optimal barrier, for any given (decreasing) curve. This gives a modeling approach for the optimal liquidation time, i.e., the optimal time at which the investor should liquidate a position to maximize the gainThis research was funded by Spanish Ministry of Economy and Competitiveness grants MTM2017-85618-P (via FEDER funds) and MTM2015-72907-EXPM D P I AGDepartamento de MatemáticasFacultad de Ciencias20202020-01-01research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/691253https://dx.doi.org/10.3390/math8010123reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/6912532026-06-23T12:46:27Z
dc.title.none.fl_str_mv A class of ito diffusions with known terminal value and specified optimal barrier
title A class of ito diffusions with known terminal value and specified optimal barrier
spellingShingle A class of ito diffusions with known terminal value and specified optimal barrier
D'Auria, Bernardo
Brownian bridge
Hamilton-Jacobi-Bellman equation
Liquidation strategy
Optimal stopping time
Matemáticas
title_short A class of ito diffusions with known terminal value and specified optimal barrier
title_full A class of ito diffusions with known terminal value and specified optimal barrier
title_fullStr A class of ito diffusions with known terminal value and specified optimal barrier
title_full_unstemmed A class of ito diffusions with known terminal value and specified optimal barrier
title_sort A class of ito diffusions with known terminal value and specified optimal barrier
dc.creator.none.fl_str_mv D'Auria, Bernardo
Ferriero, Alessandro
author D'Auria, Bernardo
author_facet D'Auria, Bernardo
Ferriero, Alessandro
author_role author
author2 Ferriero, Alessandro
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Brownian bridge
Hamilton-Jacobi-Bellman equation
Liquidation strategy
Optimal stopping time
Matemáticas
topic Brownian bridge
Hamilton-Jacobi-Bellman equation
Liquidation strategy
Optimal stopping time
Matemáticas
description In this paper, we study the optimal stopping-time problems related to a class of Ito diffusions, modeling for example an investment gain, for which the terminal value is a priori known. This could be the case of an insider trading or of the pinning at expiration of stock options. We give the explicit solution to these optimization problems and in particular we provide a class of processes whose optimal barrier has the same form as the one of the Brownian bridge. These processes may be a possible alternative to the Brownian bridge in practice as they could better model real applications. Moreover, we discuss the existence of a process with a prescribed curve as optimal barrier, for any given (decreasing) curve. This gives a modeling approach for the optimal liquidation time, i.e., the optimal time at which the investor should liquidate a position to maximize the gain
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/691253
https://dx.doi.org/10.3390/math8010123
url http://hdl.handle.net/10486/691253
https://dx.doi.org/10.3390/math8010123
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv M D P I AG
publisher.none.fl_str_mv M D P I AG
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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