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Title:Porazdelitve ekstremnih vrednosti za potrebe določanja lastnih deležev pri pozavarovanju
Authors:Cipot, Aleša (Author)
Jakovac, Marko (Mentor) More about this mentor... New window
Lesar, Marko (Co-mentor)
Files:.pdf MAG_Cipot_Alesa_2016.pdf (4,89 MB)
 
Language:Slovenian
Work type:Master's thesis/paper (mb22)
Typology:2.09 - Master's Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Magistrsko delo obravnava teorijo ekstremnih vrednosti in njene porazdelitve, ki imajo velik pomen pri modeliranju velikih premoženjskih škod v pozavarovalništvu. Delo je razdeljeno na dva dela, in sicer teoretični ter empirični del. V prvem poglavju so zapisani osnovni pojmi iz verjetnosti in statistike. V drugem poglavju je podrobneje obravnavana teorija ekstremnih vrednosti in splošna parametrična pristopa, to sta: model maksimumov skupin podatkov in model preseganja mejne vrednosti. V tretjem poglavju sta predstavljeni grafični orodji, graf kvantilov in graf povprečnih odmikov, ki nam pomagata pri določanju mejne vrednosti pri drugem parametričnem pristopu. V četrtem poglavju je definirana mera tveganja, njene lastnosti in pogosto uporabljeni meri tveganja, tvegana vrednost ter pričakovani primanjkljaj. V petem poglavju obravnavamo pozavarovanje in na kratko predstavimo oblike ter načine pozavarovalnega kritja. Teoretični del zaključujemo z uporabo teorije ekstremnih vrednosti v pozavarovalništvu. V empiričnem delu naloge je obravnavana teorija ekstremnih vrednosti na realnih podatkih izbrane zavarovalnice. Tu določimo porazdelitveno funkcijo ekstremnih škod in podamo rezultate mer tveganj, ki predstavljajo pravo dodano vrednost uporabe teorije ekstremnih vrednosti v pozavarovalništvu. Tako z grafičnimi in teoretičnimi metodami, opisanimi v prvem delu naloge, upravičimo uporabo teorije ekstremnih vrednosti na danih podatkih.
Keywords:teorija ekstremnih vrednosti, model maksimumov skupin podatkov, posplošena porazdelitev ekstremnih vrednosti, model preseganja mejne vrednosti, posplošena Paretova porazdelitev, mera tveganja, tvegana vrednost, pričakovani primanjkljaj, pozavarovanje, lastni delež.
Year of publishing:2016
Publisher:[A. Cipot]
Source:Maribor
UDC:517.9(043.2)
COBISS_ID:22341640 Link is opened in a new window
NUK URN:URN:SI:UM:DK:FDET7LBX
Views:875
Downloads:170
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:Extreme value distributions for the purpose of determining retention limits in reinsurance
Abstract:The master thesis discusses the extreme value theory and its distributions which have a great importance for the modeling of large property losses in reinsurance. The thesis is divided into two parts, namely the theoretical and the empirical part. The first chapter provides basic concepts of probability and statistics. The second chapter discusses in detail the extreme value theory and two general parametric aproaches, namely the block maxima model and the peak over threshold model. In the third chapter graphical tools are presented, the QQ-plot and the ME-plot, which help us with determining the value limits of the second parametric approach. The fourth chapter defines risk measure, its characteristics, and commonly used risk measures, value at risk and expected shortfall. In the fifth chapter we discuss reinsurance and briefly introduce forms and ways of reinsurance coverage. The theoretical part is completed with using the extreme value theory in reinsurance. The empirical part of the thesis deals with the extreme value theory on real data of the selected insurance company. Here we determine the distribution function of extreme losses and we deliver the results of risk measures, which represent the real added value of using the extreme value theory in reinsurance. Both graphical and theoretical methods described in the first part of the thesis justify the application of the extreme value theory on the given data.
Keywords:extreme value theory, block maxima model, generalized extreme value distribution, peak over threshold model, generalized Pareto distribution, risk measure, value at risk, expected shortfall, reinsurance, retention limit.


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