An algorithm to solve optimal stopping problems for onedimensional diffusions
Resumen:
Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal stopping time at which it is attained. Our approach is based on Dynkin’s characterization of the value function. The combination of Riesz’s representation of α-excessive functions and the inversion formula gives the density of the representing measure, being only necessary to determine its support. This last task is accomplished through an algorithm. The proposed method always arrives to the solution, thus no verification is needed, giving, in particular, the shape of the stopping region. Generalizations to diffusions with atoms in the speed measure and to non smooth payoffs are analyzed
| 2022 | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/41079 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522801464115200 |
|---|---|
| author | Crocce, Fabián |
| author2 | Mordecki, Ernesto |
| author2_role | author |
| author_facet | Crocce, Fabián Mordecki, Ernesto |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Crocce Fabián, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Crocce, Fabián Mordecki, Ernesto |
| dc.date.accessioned.none.fl_str_mv | 2023-11-14T12:33:49Z |
| dc.date.available.none.fl_str_mv | 2023-11-14T12:33:49Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal stopping time at which it is attained. Our approach is based on Dynkin’s characterization of the value function. The combination of Riesz’s representation of α-excessive functions and the inversion formula gives the density of the representing measure, being only necessary to determine its support. This last task is accomplished through an algorithm. The proposed method always arrives to the solution, thus no verification is needed, giving, in particular, the shape of the stopping region. Generalizations to diffusions with atoms in the speed measure and to non smooth payoffs are analyzed |
| dc.format.extent.es.fl_str_mv | 23 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Crocce, F y Mordecki, E. "An algorithm to solve optimal stopping problems for onedimensional diffusions". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2022, 19: 1353–1375. 23 h. DOI:10.30757/ALEA.v19-54 |
| dc.identifier.doi.none.fl_str_mv | 10.30757/ALEA.v19-54 |
| dc.identifier.issn.none.fl_str_mv | 1980-0436 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/41079 |
| dc.language.iso.none.fl_str_mv | en_US eng |
| dc.publisher.es.fl_str_mv | ALEA |
| dc.relation.ispartof.es.fl_str_mv | Latin American Journal of Probability and Mathematical Statistics, 2022, 19: 1353–1375 |
| 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.title.none.fl_str_mv | An algorithm to solve optimal stopping problems for onedimensional diffusions |
| 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 | Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal stopping time at which it is attained. Our approach is based on Dynkin’s characterization of the value function. The combination of Riesz’s representation of α-excessive functions and the inversion formula gives the density of the representing measure, being only necessary to determine its support. This last task is accomplished through an algorithm. The proposed method always arrives to the solution, thus no verification is needed, giving, in particular, the shape of the stopping region. Generalizations to diffusions with atoms in the speed measure and to non smooth payoffs are analyzed |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_9c21d9d026f7cc2928bffdcf0d923c59 |
| identifier_str_mv | Crocce, F y Mordecki, E. "An algorithm to solve optimal stopping problems for onedimensional diffusions". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2022, 19: 1353–1375. 23 h. DOI:10.30757/ALEA.v19-54 1980-0436 10.30757/ALEA.v19-54 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en_US |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/41079 |
| publishDate | 2022 |
| 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 | Crocce Fabián, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Mordecki Ernesto, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2023-11-14T12:33:49Z2023-11-14T12:33:49Z2022Crocce, F y Mordecki, E. "An algorithm to solve optimal stopping problems for onedimensional diffusions". Latin American Journal of Probability and Mathematical Statistics. [en línea] 2022, 19: 1353–1375. 23 h. DOI:10.30757/ALEA.v19-541980-0436https://hdl.handle.net/20.500.12008/4107910.30757/ALEA.v19-54Considering a real-valued diffusion, a real-valued reward function and a positive discount rate, we provide an algorithm to solve the optimal stopping problem consisting in finding the optimal expected discounted reward and the optimal stopping time at which it is attained. Our approach is based on Dynkin’s characterization of the value function. The combination of Riesz’s representation of α-excessive functions and the inversion formula gives the density of the representing measure, being only necessary to determine its support. This last task is accomplished through an algorithm. The proposed method always arrives to the solution, thus no verification is needed, giving, in particular, the shape of the stopping region. Generalizations to diffusions with atoms in the speed measure and to non smooth payoffs are analyzedSubmitted by Egaña Florencia (florega@gmail.com) on 2023-11-13T17:47:01Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 19-54.pdf: 608273 bytes, checksum: d23d48f2733f22fa8b7e0fd14e7c1b85 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-11-13T18:09:56Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 19-54.pdf: 608273 bytes, checksum: d23d48f2733f22fa8b7e0fd14e7c1b85 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-11-14T12:33:49Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 19-54.pdf: 608273 bytes, checksum: d23d48f2733f22fa8b7e0fd14e7c1b85 (MD5) Previous issue date: 202223 h.application/pdfen_USengALEALatin American Journal of Probability and Mathematical Statistics, 2022, 19: 1353–1375Las 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)An algorithm to solve optimal stopping problems for onedimensional diffusionsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaCrocce, FabiánMordecki, ErnestoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/41079/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/41079/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-814674http://localhost:8080/xmlui/bitstream/20.500.12008/41079/3/license_text6eed504571858d3e58aeed5ad67e191aMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | An algorithm to solve optimal stopping problems for onedimensional diffusions Crocce, Fabián |
| status_str | publishedVersion |
| title | An algorithm to solve optimal stopping problems for onedimensional diffusions |
| title_full | An algorithm to solve optimal stopping problems for onedimensional diffusions |
| title_fullStr | An algorithm to solve optimal stopping problems for onedimensional diffusions |
| title_full_unstemmed | An algorithm to solve optimal stopping problems for onedimensional diffusions |
| title_short | An algorithm to solve optimal stopping problems for onedimensional diffusions |
| title_sort | An algorithm to solve optimal stopping problems for onedimensional diffusions |
| url | https://hdl.handle.net/20.500.12008/41079 |
