Modelování výše škod v neživotním pojištění

This bachelor thesis focuses on modeling the distribution of claim severity in non-life insurance using truncated distributions. The aim of this work is to find a probability distribution of claim severity that is truncated and compare its characteristics with a real model. Three types of distributions are analyzed and compared in the thesis: log-normal, gamma, and Pareto, with an emphasis on double truncation. Two methods of point estimation were utilized for modeling - the maximum likelihood method and the method of moments. Simulations on generated data preceded the application to real data, allowing the verification of the functionality and accuracy of the estimates. The results showed that there is no clear best universal method for all types of distributions and that the selection of an appropriate method depends on the specific characteristics of the data. Based on the analysis of real data provided by the Czech Insurers’ Bureau, it was found that the chosen truncated log-normal distribution provides the most adequate model for the distribution of property damage severity within compulsory liability insurance. This thesis offers a new perspective on the use of truncated distributions in insurance and provides tools for better risk estimation, which may be beneficial for pricing and reserve formation by insurers.