Portfolio optimization with two quasiconvex risk measures

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buir.contributor.authorArarat, Çağın
buir.contributor.orcidArarat, Çağın|0000-0002-6985-7665
dc.citation.epage717en_US
dc.citation.issueNumber2en_US
dc.citation.spage695en_US
dc.citation.volumeNumber45en_US
dc.contributor.authorArarat, Çağın
dc.date.accessioned2022-02-17T11:25:35Z
dc.date.available2022-02-17T11:25:35Z
dc.date.issued2021-03-26
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractWe study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is necessary to consider the risk preferences of two parties, such as a portfolio manager and a regulator, at the same time. A special case of this problem where the risk measures are assumed to be coherent (positively homogeneous) is studied recently in a joint work of the author. The present paper extends the analysis to a more general setting by assuming that the two risk measures are only quasiconvex. First, we study the case where the principal risk measure is convex. We introduce a dual problem, show that there is zero duality gap between the portfolio optimization problem and the dual problem, and finally identify a condition under which the Lagrange multiplier associated to the dual problem at optimality gives an optimal portfolio. Next, we study the general case without the convexity assumption and show that an approximately optimal solution with prescribed optimality gap can be found by using the well-known bisection algorithm combined with a duality result that we prove.en_US
dc.description.provenanceSubmitted by Türkan Cesur (cturkan@bilkent.edu.tr) on 2022-02-17T11:25:35Z No. of bitstreams: 1 Portfolio_optimization_with_two_quasiconvex_risk_measures.pdf: 220506 bytes, checksum: 6693c8237877745cc463f6feae966573 (MD5)en
dc.description.provenanceMade available in DSpace on 2022-02-17T11:25:35Z (GMT). No. of bitstreams: 1 Portfolio_optimization_with_two_quasiconvex_risk_measures.pdf: 220506 bytes, checksum: 6693c8237877745cc463f6feae966573 (MD5) Previous issue date: 2021-03-26en
dc.identifier.doi10.3906/mat-2012-45en_US
dc.identifier.eissn1303-6149
dc.identifier.issn1300-0098
dc.identifier.urihttp://hdl.handle.net/11693/77465
dc.language.isoEnglishen_US
dc.publisherScientific and Technical Research Council of Turkey - TUBITAK,Turkiye Bilimsel ve Teknik Arastirma Kurumuen_US
dc.relation.isversionofhttps://doi.org/10.3906/mat-2012-45en_US
dc.source.titleTurkish Journal of Mathematicsen_US
dc.subjectPortfolio optimizationen_US
dc.subjectQuasiconvex risk measureen_US
dc.subjectMinimal penalty functionen_US
dc.subjectMaximal risk functionen_US
dc.subjectLagrange dualityen_US
dc.subjectBisection methoden_US
dc.titlePortfolio optimization with two quasiconvex risk measuresen_US
dc.typeArticleen_US

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