Optimal stopping of oscillating Brownian motion
Resumen:
We solve optimal stopping problems for an oscillating Brownian motion, i.e. a diffusion with positive piecewise constant volatility changing at the point x=0. Let σ1 and σ 2 denote the volatilities on the negative and positive half-lines, respectively. Our main result is that continuation region of the optimal stopping problem with reward ((1+x)+)2 can be disconnected for some values of the discount rate when 2 σ 21 <σ22. Based on the fact that the skew Brownian motion in natural scale is an oscillating Brownian motion, the obtained results are translated into corresponding results for the skew Brownian motion.
| 2019 | |
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Excessive function Integral representation of excessive functions |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/28109 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
| _version_ | 1807522786024882176 |
|---|---|
| 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 Pupko 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 | 2021-06-08T13:39:00Z |
| dc.date.available.none.fl_str_mv | 2021-06-08T13:39:00Z |
| dc.date.issued.none.fl_str_mv | 2019 |
| dc.description.abstract.none.fl_txt_mv | We solve optimal stopping problems for an oscillating Brownian motion, i.e. a diffusion with positive piecewise constant volatility changing at the point x=0. Let σ1 and σ 2 denote the volatilities on the negative and positive half-lines, respectively. Our main result is that continuation region of the optimal stopping problem with reward ((1+x)+)2 can be disconnected for some values of the discount rate when 2 σ 21 <σ22. Based on the fact that the skew Brownian motion in natural scale is an oscillating Brownian motion, the obtained results are translated into corresponding results for the skew Brownian motion. |
| dc.format.extent.es.fl_str_mv | 12 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Mordecki Pupko, E y Salminen, P. "Optimal stopping of oscillating Brownian motion". Electronic Communications in Probability. [en línea] 2019, 24(50): 1-12. 12 h. DOI: 10.1214/19-ECP250 |
| dc.identifier.doi.none.fl_str_mv | 10.1214/19-ECP250 |
| dc.identifier.issn.none.fl_str_mv | 1083-589X |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/28109 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | Institute of Mathematical Statistics and Bernoulli Society |
| dc.relation.ispartof.es.fl_str_mv | Electronic Communications in Probability, 2019, 24(50): 1-12 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución (CC - By 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 | Excessive function Integral representation of excessive functions |
| dc.title.none.fl_str_mv | Optimal stopping of oscillating Brownian motion |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | We solve optimal stopping problems for an oscillating Brownian motion, i.e. a diffusion with positive piecewise constant volatility changing at the point x=0. Let σ1 and σ 2 denote the volatilities on the negative and positive half-lines, respectively. Our main result is that continuation region of the optimal stopping problem with reward ((1+x)+)2 can be disconnected for some values of the discount rate when 2 σ 21 <σ22. Based on the fact that the skew Brownian motion in natural scale is an oscillating Brownian motion, the obtained results are translated into corresponding results for the skew Brownian motion. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_eba62bcee5e766768a10ba03b5210a5b |
| identifier_str_mv | Mordecki Pupko, E y Salminen, P. "Optimal stopping of oscillating Brownian motion". Electronic Communications in Probability. [en línea] 2019, 24(50): 1-12. 12 h. DOI: 10.1214/19-ECP250 1083-589X 10.1214/19-ECP250 |
| 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:20.500.12008/28109 |
| 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 (CC - By 4.0) |
| spelling | Mordecki Pupko Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Salminen Paavo2021-06-08T13:39:00Z2021-06-08T13:39:00Z2019Mordecki Pupko, E y Salminen, P. "Optimal stopping of oscillating Brownian motion". Electronic Communications in Probability. [en línea] 2019, 24(50): 1-12. 12 h. DOI: 10.1214/19-ECP2501083-589Xhttps://hdl.handle.net/20.500.12008/2810910.1214/19-ECP250We solve optimal stopping problems for an oscillating Brownian motion, i.e. a diffusion with positive piecewise constant volatility changing at the point x=0. Let σ1 and σ 2 denote the volatilities on the negative and positive half-lines, respectively. Our main result is that continuation region of the optimal stopping problem with reward ((1+x)+)2 can be disconnected for some values of the discount rate when 2 σ 21 <σ22. Based on the fact that the skew Brownian motion in natural scale is an oscillating Brownian motion, the obtained results are translated into corresponding results for the skew Brownian motion.Submitted by Verdun Juan Pablo (jverdun@fcien.edu.uy) on 2021-06-07T22:06:23Z No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.121419-ECP250.pdf: 258386 bytes, checksum: 8513d1bf440d45aea2d48309115a040c (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2021-06-08T13:30:03Z (GMT) No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.121419-ECP250.pdf: 258386 bytes, checksum: 8513d1bf440d45aea2d48309115a040c (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2021-06-08T13:39:00Z (GMT). No. of bitstreams: 2 license_rdf: 19875 bytes, checksum: 9fdbed07f52437945402c4e70fa4773e (MD5) 10.121419-ECP250.pdf: 258386 bytes, checksum: 8513d1bf440d45aea2d48309115a040c (MD5) Previous issue date: 201912 h.application/pdfenengInstitute of Mathematical Statistics and Bernoulli SocietyElectronic Communications in Probability, 2019, 24(50): 1-12Las 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 (CC - By 4.0)Excessive functionIntegral representation of excessive functionsOptimal stopping of oscillating Brownian motionArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaMordecki, ErnestoSalminen, PaavoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/28109/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/28109/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-838395http://localhost:8080/xmlui/bitstream/20.500.12008/28109/3/license_textd606c60c5d78967c4ed7a729e5bb402fMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Optimal stopping of oscillating Brownian motion Mordecki, Ernesto Excessive function Integral representation of excessive functions |
| status_str | publishedVersion |
| title | Optimal stopping of oscillating Brownian motion |
| title_full | Optimal stopping of oscillating Brownian motion |
| title_fullStr | Optimal stopping of oscillating Brownian motion |
| title_full_unstemmed | Optimal stopping of oscillating Brownian motion |
| title_short | Optimal stopping of oscillating Brownian motion |
| title_sort | Optimal stopping of oscillating Brownian motion |
| topic | Excessive function Integral representation of excessive functions |
| url | https://hdl.handle.net/20.500.12008/28109 |
