Μέθοδοι προσέγγισης της κατανομής των συνολικών αποζημιώσεων
Approximation methods for the distribution of aggregate claims
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Keywords
Αποζημιώσεις ; Κατανομή ; Μέθοδοι προσέγγισης ; Θεωρία κινδύνου ; Συλλογικό πρότυποAbstract
In this dissertation we examine a number of approaches that have been proposed and used in the theory of collective risk. More specifically, in the collective model of risk theory, the greatest interest is focused on the distribution of total compensation for the insurance company. Based on the literature, the calculation of this distribution is almost impossible using a closed form or even through a simple iterative process except for specific distributions of individual damages. For this reason, several approximation methods have been proposed for this calculation. Some of these methods have already been integrated, in the form of suitable algorithms in the actuar package of the R programming language and thus their implementation and evaluation becomes possible. The present dissertation utilizing models of discrete and continuous distributions uses the following approaches in order to study the issue of the distribution of total compensation: Normal approach (NA), Approach with Translated Gamma Approach (TGA), Normal Power Approach (NPA), Bowers Approach, Haldane Approach and Wilson-Hilferty Approach. The results highlight the peculiarities but also the strengths and weaknesses of each method.