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Modelling Bonus - Malus Systems
Stroukalová, Marika ; Mazurová, Lucie (advisor) ; Prokešová, Michaela (referee)
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
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Modelling Bonus - Malus Systems
Stroukalová, Marika ; Mazurová, Lucie (advisor) ; Prokešová, Michaela (referee)
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
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The analysis of the vehicle insurance
Malá, Markéta ; Radová, Jarmila (advisor) ; Vohralík, Michal (referee)
The bachelor thesis is focused on the analysis of the vehicle insurance in the Czech Republic. In the theoretical section the author deals with compulsory motor third party liability insurance and motor own damage insurance. Theme is a very actual, because of the variability of the market situation, insurance companies create variability within the competitiveness and trying to obtain client. The practical part of thesis deals with the examining the Czech financial market. The author of the thesis focuses on four selected insurance companies according to total premiums written on the compulsory motor third party liability insurance and motor own damage insurance. In the practical part are two examples, on those potential candidates could see the influence of factors. The author of the thesis in the last part wants to find out advantage of the combined product, compared to negotiation of the compulsory motor third party liability insurance and the motor own damage insurance separately.
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Does Bonus-Malus System Encourage Drivers to be More Responsible on the Roads?
Línová, Veronika ; Hudík, Marek (advisor) ; Šťastný, Daniel (referee)
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.
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