Universität zu Köln

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:	Creators Email ORCID ORCID Put Code Bazovkin, Pavlo P.Bazovkin@yandex.com UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-70408
Date:	2014
Language:	English
Faculty:	Faculty of Management, Economy and Social Sciences
Divisions:	Faculty of Management, Economics and Social Sciences > Economics > Econometrics and Statistics > Professorship for Statistics and Econometrics
Subjects:	Data processing Computer science General statistics Mathematics Management and auxiliary services
Uncontrolled Keywords:	Keywords Language Coherent risk measures; applied statistics; computational geometry; portfolio selection; robust optimization; multivariate data analysis; non-parametric models English
Date of oral exam:	17 November 2014
Referee:	Name Academic Title Mosler, Karl Prof. Dr. Breitung, Jörg Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/7040