Applications of Markov chains and convex sets in ridk management

Abstract

In this dissertation we examine the conditions under which a model with a large number of elements can be approximated by a new, simpler one, consisting of a smaller number of elements, without missing the qualitative features of the initial model. The certain conditions facilitate the analysis of large and complex systems that are widely used in studies. We apply our research in two important tools for credit risk management: credit ratings and credit scoringParticularly, we first introduce Markov Chains as a model of the stochastic evolution of credit ratings and then consider the conditions under which a Markov chain is lumpable. We review briefly the definition and characterization of an exactly lumpable Markov chain and through an example of a credit migration matrix we show that in general these conditions are not satisfied. We then introduce the concept of approximate lumpability, and we propose a procedure for finding a lumpable Markov chain that is the closest approximation of ...
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DOI
10.12681/eadd/34686
Handle URL
http://hdl.handle.net/10442/hedi/34686
ND
34686
Alternative title
Εφαρμογές αλυσίδων Markov και κυρτών συνόλων στη διαχείριση κινδύνου
Author
Loizides, Marios of Ioannis
Date
2014
Degree Grantor
Athens University Economics and Business (AUEB)
Committee members
Γιαννακόπουλος Αθανάσιος
Πανάς Επαμεινώνδας
Φράγκος Νικόλαος
Ψαράκης Στυλιανός
Μούρτος Ιωάννης
Pinto Alberto
Moguerza Javier Martinez
Discipline
Social SciencesEconomics and Business
Keywords
Markov chains; Linear separation of hyperplanes; Credit rating; Credit scoring; Lumping Markov chains; Convex sets; Kirchberger's theorem; Approximate lumpability
Country
Greece
Language
English
Description
vii, 105 σ., tbls., ind.
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