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Risk measures - sensitivity and dynamics
dc.creatorBranda, Martin
dc.date.accessioned2021-05-19T15:32:47Z
dc.date.available2021-05-19T15:32:47Z
dc.date.issued2008
dc.identifier.urihttp://hdl.handle.net/20.500.11956/15188
dc.description.abstractRisk measures are subject to many scientific papers and monographs published on financial portfolio optimization problem within stochastic programming. Currently there are many functionals which measure risk of random future losses according to risk managers preferences. However, their sensitivity is studied less commonly, especially according to possible changes of input data or with respect to the portfolio allocation. This thesis deals with sensitivity of two frequently discussed measures - Value at Risk (VaR) and Conditional Value at Risk (CVaR). Explicit contamination bounds for relative VaR optimization problem are expressed using general results of parametric optimization valid for quadratic programming. A numerical study and a heuristic algorithm for correlation matrices stressing are involved. Sensitivity of VaR and CVaR is studied through their derivatives with respect to the portfolio allocation. Assumptions for the derivatives are formulated, Hessians introduced and convexity is discussed. At last, some dynamic risk measures for multi-period investory models are proposed.en_US
dc.languageČeštinacs_CZ
dc.language.isocs_CZ
dc.publisherUniverzita Karlova, Matematicko-fyzikální fakultacs_CZ
dc.titleMíry rizika-dynamika, citlivostcs_CZ
dc.typerigorózní prácecs_CZ
dcterms.created2008
dcterms.dateAccepted2008-05-26
dc.description.departmentDepartment of Probability and Mathematical Statisticsen_US
dc.description.departmentKatedra pravděpodobnosti a matematické statistikycs_CZ
dc.description.facultyFaculty of Mathematics and Physicsen_US
dc.description.facultyMatematicko-fyzikální fakultacs_CZ
dc.identifier.repId60043
dc.title.translatedRisk measures - sensitivity and dynamicsen_US
dc.identifier.aleph000983718
thesis.degree.nameRNDr.
thesis.degree.levelrigorózní řízenícs_CZ
thesis.degree.disciplineProbability, mathematical statistics and econometricsen_US
thesis.degree.disciplinePravděpodobnost, matematická statistika a ekonometriecs_CZ
thesis.degree.programMathematicsen_US
thesis.degree.programMatematikacs_CZ
uk.thesis.typerigorózní prácecs_CZ
uk.taxonomy.organization-csMatematicko-fyzikální fakulta::Katedra pravděpodobnosti a matematické statistikycs_CZ
uk.taxonomy.organization-enFaculty of Mathematics and Physics::Department of Probability and Mathematical Statisticsen_US
uk.faculty-name.csMatematicko-fyzikální fakultacs_CZ
uk.faculty-name.enFaculty of Mathematics and Physicsen_US
uk.faculty-abbr.csMFFcs_CZ
uk.degree-discipline.csPravděpodobnost, matematická statistika a ekonometriecs_CZ
uk.degree-discipline.enProbability, mathematical statistics and econometricsen_US
uk.degree-program.csMatematikacs_CZ
uk.degree-program.enMathematicsen_US
thesis.grade.csUznánocs_CZ
thesis.grade.enRecognizeden_US
uk.abstract.enRisk measures are subject to many scientific papers and monographs published on financial portfolio optimization problem within stochastic programming. Currently there are many functionals which measure risk of random future losses according to risk managers preferences. However, their sensitivity is studied less commonly, especially according to possible changes of input data or with respect to the portfolio allocation. This thesis deals with sensitivity of two frequently discussed measures - Value at Risk (VaR) and Conditional Value at Risk (CVaR). Explicit contamination bounds for relative VaR optimization problem are expressed using general results of parametric optimization valid for quadratic programming. A numerical study and a heuristic algorithm for correlation matrices stressing are involved. Sensitivity of VaR and CVaR is studied through their derivatives with respect to the portfolio allocation. Assumptions for the derivatives are formulated, Hessians introduced and convexity is discussed. At last, some dynamic risk measures for multi-period investory models are proposed.en_US
uk.file-availabilityV
uk.grantorUniverzita Karlova, Matematicko-fyzikální fakulta, Katedra pravděpodobnosti a matematické statistikycs_CZ
thesis.grade.codeU
uk.publication-placePrahacs_CZ
uk.thesis.defenceStatusU


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