This thesis is focused on the question whether implementing of a malus policy into a bonus-malus system encourages drivers to be more responsible on the road. The drivers should be motivated to change their behaviour be aimed at decrease of reported insurance events because this system increases their premium whenever they are in an accident. To answer the given problem I used regression analysis with a random effects model and I analysed the drivers registered at insurance company Allianz in years 2000 - 2005. The result of this analysis shows that there was no change in the behaviour since the malus policy was introduced. The examined impact has been detected in case which was interacting with a different variable. The malus policy had the impact on a reduction of accidents in regions below 10 000 inhabitants. This thesis is also focused on the influence of driver characteristic and technical properties of his vehicle on reported insurance events. Tested variables are sex of the drivers, region of driver's residence, age and engine capacity. All explanatory variables have effect on the reported insurance events.

Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1

Global warming issues are a widespread problem around the world and the emissions of greenhouse gases is one of the main contributors. The transport sector emits a significant amount of greenhouse gas emissions; thus, this contributes to global warming. To tackle this challenge the Swedish state introduced in July 2018 a system called bonus-malus system which aims to increase the proportion of eco-friendly cars and in the long run reducing greenhouse gases emissions from the transport sector. This paper examines the tax system within the Bonus-Malus system. Primarily investigating if Malus, tax system, impacted the demand for electric vehicles since it introduced. The study conducted based on a short panel data from Sweden´s 21 counties for the period 2016-2020 and the analysis method applied is a regression analysis. The results of this thesis confirm a strong positive relationship between the share of newly registered battery electric vehicles (BEV) and the Malus, but much weaker influence of the other studied variables. Suggesting that tax system induce on emission seem to be efficient at boost the demand for BEV