Matematični model za izračun tehnične premije

diplomsko delo

Doroteja Leskovar (Author), Marko Jakovac (Mentor)

Abstract

V diplomskem delu je predstavljen matematični model za izračun tehnične premije. V uvodnem poglavju so vpeljane osnove verjetnostnega računa. V drugem poglavju sta opisani dve slučajni spremenljivki, pomembni za gradnjo verjetnostnega modela, in sicer število škod in višina škod. S pomočjo primerov so vpeljane enačbe za izračun osnovnih karakteristik teh dveh slučajnih spremenljivk. Le-te so potrebne za strukturo porazdelitvene funkcije. V naslednjem poglavju je definirana struktura premije in izračun neto premije. Da zavarovalnica lahko določi višino premije, mora poznati tveganje, ki ga prevzema. Komponente za določanje tveganja so zavarovalna vsota, škodni indeks, verjetnostna porazdelitev celotnega izplačila in varnostni dodatek. V zadnjem poglavju sta definirani dejanska škoda in višina zahtevka. Določene so osnovne postavke neto premije, ki povečana za varnostni dodatek tvori tehnično premijo. Vpeljano je premijsko načelo, ki se lahko uporabi za izračun ustrezne višine varnostnega dodatka. Opisana so različna premijska načela, in sicer načelo pričakovane vrednosti, načelo variance, načelo standardnega odklona in načelo kvantilov, s katerimi definiramo izračun tehnične premije.

Keywords

matematika;neto premija;tveganje;tehnična premija;verjetnost;osnove;škoda;višina;število škod;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2013
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[D. Leskovar]
UDC:	51(043.2)
COBISS:	19980552
Views:	2029
Downloads:	204
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Mathematical model for the technical premium calculation
Secondary abstract:	The diploma presents the mathematical model for the technical premium calculation. Introductory chapter explains the basics of probability. The second chapter describes two random variables important for constructing a probability model, the loss amount and the claim amount. With the help of examples, equations for calculating basic characteristics of those two random variables are introduced. They are necessary to structure a distributional function. Premium structure and net premium calculation is defined in the next chapter. Insurance company needs to know the risks it takes so that it can determine the premium. Components for determining the risk are sum insured, the risk index, probability distribution of total payment and the safety loading. The last chapter defines actual loss and claim amount. The basics of net premium are set, which, enlarged for the safety loading, form the technical premium. Premium principle which can be used to calculate the sufficient height of the safety loading is explained. There are also descriptions of premium principles: expected value principle, variance principle, standard deviation and percentile principle which we use to define a technical premium calculation.
Secondary keywords:	net premium;risk;technical premium;basic probability;claim amount;loss amount.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VIII, 55 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	81863