Kopule in odvisnost avtomobilskih zavarovanj

magistrsko delo

Tamara Šarh (Author), Marko Jakovac (Mentor), Matej Skernišak (Co-mentor)

Abstract

V magistrskem delu obravnavamo odvisnost avtomobilskih zavarovanj, natančneje zavarovanje avtomobilskega kaska in avtomobilske odgovornosti. Magistrsko delo je razdeljeno na dva dela, teoretični in praktični primer. V prvem delu so opisani osnovni pojmi s področja verjetnosti in statistike, predstavljena so neživljenjska zavarovanja s poudarkom na avtomobilskih zavarovanjih, zapisane so pomembne definicije in izrek s področja teorije kopul ter definirane različne mere odvisnosti. Praktični primer temelji na analizi odvisnosti dveh naključnih spremenljivk, avtomobilskega kaska in avtomobilske odgovornosti. Za naključni spremenljivki poiščemo pripadajoči porazdelitveni funkciji in izračunamo različne mere odvisnosti med spremenljivkama, nato za izbrani naključni spremenljivki, z ustreznimi knjižnicami v programu R, poiščemo kopulo, ki najboljše opiše odnos med spremenljivkama. Simuliramo dva naključna vzorca kopul, prvi za družino kopul, ki jo izbere program R, ter drugega za kopulo Clayton, izbrano po lastni presoji. Iščemo ustreznejšo družino kopul. Postopek reševanja ponovimo za različne skupine določene glede na vrsto škodnega primera. Ključne ugotovitve so zapisane v zadnjem poglavju.

Keywords

magistrska dela;avtomobilsko zavarovanje;zavarovanje avtomobilskega kaska;zavarovanje avtomobilske odgovornosti;kopula;odvisnost;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[T. Šarh]
UDC:	519.2(043.2)
COBISS:	24941064
Views:	732
Downloads:	61
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Copulas and dependence of car insurances
Secondary abstract:	In the master thesis we discuss dependence of car insurances, more speciifcally dependence between the motor vehicle damage insurance and the motor vehicle liability insurance. The thesis is divided into the theoretical part and a practical example. In first part we describe basic concepts of probability and statistics, we present nonlife insurances with emphasis on car insurances, we describe significant definitions and theorems of copulas and define diferent measures of dependence. Practical example is based on analysis of dependence between two random variables, the motor vehicle damage insurance and the motor vehicle liability insurance. We obtain the distribution of the two random variables and calculate diferent measures of dependence between the two random variables. In the next step we select a copula, using corresponding packages in program R, which might describe joint behavior of the two variables. Then we generate two random samples using copulas, one for the copula family selected by the program R, and second for the Clayton copula. We try to determine which copula fits best. Described procedure is repeated for diferent groups, which are determined depending on the type of loss. Key findings are described in the last chapter.
Secondary keywords:	master theses;car insurance;motor vehicle damage insurance;motor vehicle liability insurance;copola;dependence;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 84 f., [15] f. pril.
ID:	11232634