Universität zu Köln

Geometrical Methods in Multivariate Risk Management: Algorithms and Applications

Bazovkin, Pavlo (2014) Geometrical Methods in Multivariate Risk Management: Algorithms and Applications. PhD thesis, Universität zu Köln.

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    Abstract

    This thesis builds a framework for evaluating downside risk from multivariate data via a special class of risk measures (RM). The peculiarity of the analysis lies in getting rid of strong data distributional assumptions and in orientation towards the most critical data in risk management: those with asymmetries and heavy tails. At the same time, under typical assumptions, such as the ellipticity of the data probability distribution, the conformity with classical methods is shown. The constructed class of RM is a multivariate generalization of the coherent distortion RM, which possess valuable properties for a risk manager. The design of the framework is twofold. The first part contains new computational geometry methods for the high-dimensional data. The developed algorithms demonstrate computability of geometrical concepts used for constructing the RM. These concepts bring visuality and simplify interpretation of the RM. The second part develops models for applying the framework to actual problems. The spectrum of applications varies from robust portfolio selection up to broader spheres, such as stochastic conic optimization with risk constraints or supervised machine learning.

    Item Type: Thesis (PhD thesis)
    Creators:
    CreatorsEmail
    Bazovkin, PavloP.Bazovkin@yandex.com
    URN: urn:nbn:de:hbz:38-70408
    Subjects: Data processing Computer science
    General statistics
    Mathematics
    Management and auxiliary services
    Uncontrolled Keywords:
    KeywordsLanguage
    Coherent risk measures; applied statistics; computational geometry; portfolio selection; robust optimization; multivariate data analysis; non-parametric modelsEnglish
    Faculty: Wirtschafts- u. Sozialwissenschaftliche Fakultät
    Divisions: Wirtschafts- u. Sozialwissenschaftliche Fakultät > Institut für Ökonometrie und Statistik
    Language: English
    Date: 2014
    Date Type: Publication
    Date of oral exam: 17 November 2014
    Full Text Status: Public
    Date Deposited: 14 Nov 2016 10:59:40
    Referee
    NameAcademic Title
    Mosler, KarlProf. Dr.
    Breitung, JörgProf. Dr.
    URI: http://kups.ub.uni-koeln.de/id/eprint/7040

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