Modelování pojistných škod v rámci havarijního pojištění

Abstract

The diploma thesis is focused on modelling of claim severity for a motor hull insurance portfolio. The aim of the thesis is to create and estimate a regression model for modelling of individual claim severity for a given insurance portfolio, moreover, the accuracy and the quality of the regression model has to be analyzed. The thesis is divided into five chapters, while the first chapter is dedicated to an introduction and the last chapter to a conclusion. The theoretical part is discussed in the second and the third chapter, the practical part is later described in the fourth chapter. The second chapter deals with the insurance risk management, and in the third chapter is outlined the methodology essential to regression model formation and verifying its accuracy. The fourth chapter is devoted to the resolution procedure of the optimization problem, particularly, to modelling individual claim severity. Firstly, there is a specification of the insurance data. Furthermore, we deal with formation and estimation of two regression models according to generalized linear models theory and extreme value theory. It is assumed here that individual claim severity follows neither the gamma distribution nor mixed distribution, which comprises of gamma distribution and generalized Pareto distribution. The parameters of both regression models are estimated using maximum likelihood method. The accuracy of the regression models is consequently evaluated by the analysis of raw and Pearson residuals. Finally, the regression models are compared and their quality and goodness of fit are assessed, as well.