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Distributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation

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authorProfile.id.code200720140es_CO
dc.contributor.advisorJunca Peláez, Mauricio José
dc.contributor.authorFonseca Valero, Diego Fernando
dc.contributor.id79981918es_CO
dc.contributor.juryAvella Medina, Marco
dc.contributor.juryDíaz Díaz, Mateo
dc.contributor.juryQuiroz Salazar, Adolfo José
dc.date.accessioned2023-08-04T22:18:50Z
dc.date.available2023-08-04T22:18:50Z
dc.date.issued2023-04-14
dc.descriptionEste trabajo fue elaborado como uno de los requisitos para obtener el título de doctor en matemáticas. Adicionalmente, la investigación desarrollada no presenta ningún tipo de conflicto de intereses.
dc.description.abstractThis Ph.D. thesis explores stochastic optimization from a Distributionally Robust perspective, focusing on two significant themes: the innovative use of decision variable-dependent ambiguity sets in Distributionally Robust optimization (DRO), and the estimation of the mode of a random vector using the DRO perspective. Regarding the first topic, new techniques utilizing p-Wasserstein metrics in stochastic programming are proposed, where ambiguity sets are uniquely decision variable-dependent. These developments, under certain assumptions, can be reduced to finite-dimensional optimization problems, sometimes convex. They are tested within the portfolio optimization context against standard methodologies. The research also extends to stochastic programming with expected value constraints, setting feasibility criteria relative to the Wasserstein radius and constraint parameters, and benchmarking model performance using both simulated and real financial market data. Additionally, in the realm of mode estimation, an innovative strategy is devised for identifying a mode estimator in a random vector sample, even in the absence of known probability distribution or density function. This strategy employs a DRO approach and Wasserstein distance, demonstrating the resulting estimator is consistent.
dc.description.degreelevelDoctoradoes_CO
dc.description.degreenameDoctor en Matemáticas
dc.description.researchareaApplied mathematicses_CO
dc.format.extent109es_CO
dc.format.mimetypeapplication/pdfes_CO
dc.identifier.doi10.57784/1992/69263
dc.identifier.instnameinstname:Universidad de los Andeses_CO
dc.identifier.reponamereponame:Repositorio Institucional Sénecaes_CO
dc.identifier.repourlrepourl:https://repositorio.uniandes.edu.co/es_CO
dc.identifier.urihttps://hdl.handle.net/1992/69263
dc.language.isoenges_CO
dc.publisherUniversidad de los Andeses_CO
dc.publisher.departmentDepartamento de Matemáticases_CO
dc.publisher.facultyFacultad de Cienciases_CO
dc.publisher.programDoctorado en Matemáticases_CO
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.rights.coarhttp://purl.org/coar/access_right/c_abf2
dc.rights.licenseAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
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dc.subject.keywordDistributionally robust optimization
dc.subject.keywordWasserstein metric
dc.subject.keywordConditional value at risk
dc.subject.keywordStochastic optimization
dc.subject.themesMatemáticases_CO
dc.titleDistributionally robust optimization: a novel approach with decision-dependent ambiguity sets and an application to mode estimation
dc.typeTrabajo de grado - Doctoradoes_CO
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