Optimal stopping of Brownian motion with broken drift
Resumen:
We solve an optimal stopping problem where the underlying diffusion is Brownian motion on R with a positive drift changing at zero. It is assumed that the drift μ1 on the negative side is smaller than the drift μ2 on the positive side. The main observation is that if μ2 − μ1 > 1/2 then there exists values of the discounting parameter for which it is not optimal to stop in the vicinity of zero where the drift changes. However, when the discounting gets bigger the stopping region becomes connected and contains zero. This is in contrast with results concerning optimal stopping of skew Brownian motion where the skew point is for all values of the discounting parameter in the continuation region.
| 2019 | |
| Mathematics - Probability | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/33767 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522792980086784 |
|---|---|
| author | Mordecki, Ernesto |
| author2 | Salminen, Paavo |
| author2_role | author |
| author_facet | Mordecki, Ernesto Salminen, Paavo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Salminen Paavo |
| dc.creator.none.fl_str_mv | Mordecki, Ernesto Salminen, Paavo |
| dc.date.accessioned.none.fl_str_mv | 2022-09-12T13:24:58Z |
| dc.date.available.none.fl_str_mv | 2022-09-12T13:24:58Z |
| dc.date.issued.none.fl_str_mv | 2019 |
| dc.description.abstract.none.fl_txt_mv | We solve an optimal stopping problem where the underlying diffusion is Brownian motion on R with a positive drift changing at zero. It is assumed that the drift μ1 on the negative side is smaller than the drift μ2 on the positive side. The main observation is that if μ2 − μ1 > 1/2 then there exists values of the discounting parameter for which it is not optimal to stop in the vicinity of zero where the drift changes. However, when the discounting gets bigger the stopping region becomes connected and contains zero. This is in contrast with results concerning optimal stopping of skew Brownian motion where the skew point is for all values of the discounting parameter in the continuation region. |
| dc.description.es.fl_txt_mv | Versión permitida: prepint. Wiley |
| dc.format.extent.es.fl_str_mv | 13 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Mordecki, E y Salminen, P. "Optimal stopping of Brownian motion with broken drift"[Prepint]. Publicado en: High Frequency, 2019, 2(2): 113-120.DOI:10.1002/hf2.10034 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/33767 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Mathematics - Probability |
| dc.title.none.fl_str_mv | Optimal stopping of Brownian motion with broken drift |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Versión permitida: prepint. Wiley |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_61e0f994f77fb73e916be93f56ef8144 |
| identifier_str_mv | Mordecki, E y Salminen, P. "Optimal stopping of Brownian motion with broken drift"[Prepint]. Publicado en: High Frequency, 2019, 2(2): 113-120.DOI:10.1002/hf2.10034 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/33767 |
| publishDate | 2019 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Salminen Paavo2022-09-12T13:24:58Z2022-09-12T13:24:58Z2019Mordecki, E y Salminen, P. "Optimal stopping of Brownian motion with broken drift"[Prepint]. Publicado en: High Frequency, 2019, 2(2): 113-120.DOI:10.1002/hf2.10034https://hdl.handle.net/20.500.12008/33767Versión permitida: prepint. WileyWe solve an optimal stopping problem where the underlying diffusion is Brownian motion on R with a positive drift changing at zero. It is assumed that the drift μ1 on the negative side is smaller than the drift μ2 on the positive side. The main observation is that if μ2 − μ1 > 1/2 then there exists values of the discounting parameter for which it is not optimal to stop in the vicinity of zero where the drift changes. However, when the discounting gets bigger the stopping region becomes connected and contains zero. This is in contrast with results concerning optimal stopping of skew Brownian motion where the skew point is for all values of the discounting parameter in the continuation region.Submitted by Egaña Florencia (florega@gmail.com) on 2022-09-07T18:43:28Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1811.05738.pdf: 316313 bytes, checksum: 68d9a04c122d90da3f8c819da63137eb (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2022-09-09T10:59:08Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1811.05738.pdf: 316313 bytes, checksum: 68d9a04c122d90da3f8c819da63137eb (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2022-09-12T13:24:58Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 1811.05738.pdf: 316313 bytes, checksum: 68d9a04c122d90da3f8c819da63137eb (MD5) Previous issue date: 201913 h.application/pdfenengLas obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Mathematics - ProbabilityOptimal stopping of Brownian motion with broken driftPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaMordecki, ErnestoSalminen, PaavoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/33767/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/33767/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-838616http://localhost:8080/xmlui/bitstream/20.500.12008/33767/3/license_text36c32e9c6da50e6d55578c16944ef7f6MD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Optimal stopping of Brownian motion with broken drift Mordecki, Ernesto Mathematics - Probability |
| status_str | submittedVersion |
| title | Optimal stopping of Brownian motion with broken drift |
| title_full | Optimal stopping of Brownian motion with broken drift |
| title_fullStr | Optimal stopping of Brownian motion with broken drift |
| title_full_unstemmed | Optimal stopping of Brownian motion with broken drift |
| title_short | Optimal stopping of Brownian motion with broken drift |
| title_sort | Optimal stopping of Brownian motion with broken drift |
| topic | Mathematics - Probability |
| url | https://hdl.handle.net/20.500.12008/33767 |
