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master's thesis
Markovljevi lanci u kreditnim rizicima
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. urn:nbn:hr:126:574673
Živković, Antonija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Živković, A. (2017). Markovljevi lanci u kreditnim rizicima (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:574673

Živković, Antonija. "Markovljevi lanci u kreditnim rizicima." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:574673

Živković, Antonija. "Markovljevi lanci u kreditnim rizicima." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:574673

Živković, A. (2017). 'Markovljevi lanci u kreditnim rizicima', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 02 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:574673

Živković A. Markovljevi lanci u kreditnim rizicima [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2025 January 02] Available at: https://urn.nsk.hr/urn:nbn:hr:126:574673

A. Živković, "Markovljevi lanci u kreditnim rizicima", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:574673

Metadata
TitleMarkovljevi lanci u kreditnim rizicima
Title (english)Markov Chains in Credit Risk
AuthorAntonija Živković
MentorNenad Šuvak (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2017-02-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Cilj ovog diplomskog rada je objasniti vezu izmedu Markovljevih lanaca i kreditnog rizika. Kako za Markovljeve lance u diskretnom vremenu, tako i za one u neprekidnom potrebno je procijeniti prijelazne vjerojatnosti. Prijelazne vjerojatnosti su procijenjene različitim metodama. U neprekidnom vremenu je to metoda MLE, a u diskretnom radimo s multinomnim procjeniteljima. Prijelazi koji su promatrani su prijelazi tvrtki izmedu različitih rejting kategorija, a najviše smo se fokusirali na vjerojatnost prijelaza iz određene rejting kategorije u kategoriju defaulta. Također su promatrane razlike izmedu procjenitelja u diskretnom i u neprekidnom vremenu, te se boljim pokazao procjenitelj u neprekidnom vremenu. U diskretnom vremenu je razvijen Mover-stayer model koji uključuje dva Markovljeva lanca. Procijenili smo paramtere tog modela i usporedili ih na primjeru. Na kraju izveli smo još jedan Markovljev model u diskretnom vremenu, ali na temelju bihevioralnog skora. Kako bi takav model bio dobar, potrebno je uključiti Markovljeve lance višeg reda, ali to je izvan granica rada.
Abstract (english)
The aim of this paper is to explain the relationship between Markov chains and credit risk. Transition probabilities need to be estimated for Markov chains in discrete time as well as in continuous time. Transition probabilities were estimated with two different methods, MLE method in continuous time, and multinomial estimator in discrete time. Observed transitions were transitions of companies between different rating categories and we were focused on the probability of transition from certain rating category to the category of default. We also observed differences between estimators in discrete and continuous time, and the better estimator was the one in continuous time. Moverstayer was developed model in discrete time and it includes two Markov chains. We estimated parameters of the model and compare them in one example. Finally, we developed one more Markov model in discrete time, but this one is based on the behavioral score. In order for a model to be good, it should include second order Markov chains, but that is outside the boundaries of this work.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:574673
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-02-28 12:48:45