Modelování pojistných škod v oblasti havarijního pojištění

Abstract

The doctoral dissertation thesis is focused on modelling of claims in the case of a motor hull insurance portfolio. The aim of the doctoral dissertation thesis is an application and verification of selected mathematical models, which are widely used for modelling of claims in non-life insurance, especially hull claims portfolios. These models and their determination are crucial for the findings to the fundamental characteristics of the insurance portfolio. It contributes to the pricing, and also for determining the amount of the regulatory capital requirement. The sub-objective of the doctoral thesis is to assess the influence of categorical variables as a simplification on insurance premium calculation. The real data are applied to all calculations of accident insurance in the Czech Republic territory. Particularly, the doctoral dissertation thesis has analysed the issue of models of claim frequency, the amount of individual claim severity, the model of total claim amounts, and generalised linear models. The management of risk, including fundamentals and insurance, is described in chapter 2. The models of damages are defined in chapter 3. First, the model of individual damage, including the appropriate discrete probability distribution, is specified. The model of the individual amount of the accident, including continuous probability distribution, is formulated. After this, the model of the total claims, including compound probability distribution, is described. Chapter 4 is devoted to the regression analysis and generalised linear regression model. The basic concept of this model, including the estimation methods, which is the maximum likelihood method, is described as well. Chapter 5 includes the practical component. Firstly, the data sample used for estimation is described. After that, the models themselves are estimated, first collectively and then categorically. All results are commented on comprehensively. It was found that for the estimation of the claim frequency, the most suitable the negative probability distribution was verified. For the estimation of the claim severity model, the gamma probability distribution was verified. In the case of claims frequency in the context of multivariate analysis, it was found that the most significant impact on the dependent variable has variables agecar and price. In the model of claim severity, it was found that the greatest impact on the dependent variable has variables agecar and fuel. The premium has been determined, and it can be concluded that the calculation of premiums for the non-categorised model came out the best. However, in the insurance practice, the categorisation of data, especially in non-life insurance, is of high importance and necessity, for effectiveness to the management of the portfolio. It turned out that the categorised model is a suitable approximation of the continuous model.