Sebaran Stasioner Pada Sistem Bonus-malus Swiss Serta Modifikasinya (Stationary Distribution of Swiss Bonus-malus System and Its Modification)

Bonus-Malus System is a system in actuary that introduce the premium class (state) partition, where the state is influenced by the number of annual claims reported by the policy holder. We could base the determination of the state on the stationary distribution that represent the number of policy holders in any state. Swiss Bonus-Malus System has 22 state. The number of state that involved in this system result in the difficulty of stationary distribution determination. Therefore, the aim of this paper is to study a method to obtain stationary distribution of Swiss Bonus-Malus System by recursive formula, with this recursive formula, the stationary distribution of Swiss Bonus-Malus System can be determined easier. Modification of this system with infinite state result in the changes of recursive formula to obtain the stationary. This changes including the determining of base value of the recursive formula

ROMANIAN COMPULSORY MOTOR THIRD PARTY LIABILITY INSURANCE IN 2010 AND THE PREDICTABLE FUTURE

Insurance coverage is mandatory for the motor’s owners. Analyzing the condition of theinsurance market trough 2010, by the gross written insurance premiums and the losses compensationsin the same period, the study analyzes the Romanian bonus-malus system, by comparing it with thebonus-malus system of other states. The study reveals the impact of bonus-malus clause, and also theimpact of the economic and financial crisis upon insurance market, the insufficiencies of the MTPLsystem and the ways of improving it. In the last part of this study, we analyze the future changes thatthe insurance companies have to make in according with the elimination of the discrimination troughgender in this insurance field.mandatory insurance, insurance premium, Romanian bonus-malus system

Functions of the bonus-malus system in the motor third party liability insurance of motor vehicle owners

The bonus-malus system is one of the stages of the ratemaking process in motor liability insurance. The purpose of the work is to discuss the role of the bonus-malus systems in the ratemaking and to present their functions. The article reviews the measures for assessment of the ratemaking function of the bonus-malus systems and attempts to investigate the impact of preventive and marketing functions. These functions fulfil their role under the condition that the insured party is aware of the functioning of the bonus-malus system. It has been hypothesized that the policyholders choosing the insurer do not know the bonus-malus system offered to them and that increasing the knowledge about the functioning of the system intensifies the impact of its preventive function. The study was conducted on the basis of an analysis of the insurance conditions offered by the insurers on the Polish market (GIT) and a questionnaire survey. Mathematical statistics methods have been used for the analysis. The results of the research confirm the hypothesis that the insured do not know the bonus-malus system while choosing an insurer. This is the effect of not passing enough information to the client. The results allow claiming that even offering brief information about the rules of the functioning of the bonus-malus system improves the awareness of policyholders and increases the impact of the preventive function, which makes it possible to positively verify the second research hypothesis

Efisiensi Sistem Bonus Malus Sebagai Model Rantai Markov

. Developed bonus malus system (BMS) is to make the premium paid by insured will be as closed as possible with expected occurrence of claim in every year basis. To study the efficiency of a BMS, we must previously observe the effect of claim frequency on value of premium. The efficiency of Bonus Malus System can be found through its Markov model; that is by found a stationary distribution in form of line vectors of its BMS Markov chain with its components as a function of claim frequency. In this paper, the BMS used is that of Brazil

Українська система бонус-малус: оцінка жорсткості та порівняльний аналіз з системами інших країн

Розкрито сутність і призначення системи бонус-малус в автотранспортному страхуванні; охарактеризовано українську систему бонус-малус як систему з «відсутністю пам’яті»; проведено аналіз оцінки жорсткості системи за допомогою показника відносного стаціонарного середнього рівня страхової премії у порівнянні з іншими країнами.Раскрыто сущность и предназначение системы бонус-малус а автотранспортном страховании; охарактеризовано украинскую систему бонус-малус как систему с «отсутствием памяти»; проведен анализ оценки жесткости системы с помощью показателя относительного стационарного уровня страховой премии в сравнении с другими странами.The nature and purpose of the bonus-malus system in a sector of motor insurance are investigated, the Ukrainian bonus-malus system is characterized as the system «without memory», the severity rating of the system using relative stationary average level is analyzed in comparison with other countries

Pricing automobile insurance using mixed Poisson distributions

Automobile insurance, particularly motor third liability insurance covers dominant share in the portfolio of non-life insurance in almost all countries of the world. The aim of this paper is to analyze the process of determining premium rates in automobile liability insurance using the bonus-malus system as one of the key instruments to increase traffic safety. The paper presents a brief analysis of the automobile liability insurance market in Serbia, with special reference to the bonus-malus system introduced in practice. Using a sample from the year 2015 provided by one of the biggest Serbian automobile liability insurer it has been proved that the mixed Poisson distibutions are appropriate choice in the process of modeling of the afore mentioned tariff system. The main result of the study is the construction of bonus - malus system based on mixed Poisson models, where expected value principle is used to determine the net premium. According to the analysis, it has been concluded that during the creation of a bonus-malus system in practice it is important to use certain mathematical and statistical models, as well as that the existing tariff system of automobile liabili

Pricing automobile insurance using mixed Poisson distributions

Automobile insurance, particularly motor third liability insurance covers dominant share in the portfolio of non-life insurance in almost all countries of the world. The aim of this paper is to analyze the process of determining premium rates in automobile liability insurance using the bonus-malus system as one of the key instruments to increase traffic safety. The paper presents a brief analysis of the automobile liability insurance market in Serbia, with special reference to the bonus-malus system introduced in practice. Using a sample from the year 2015 provided by one of the biggest Serbian automobile liability insurer it has been proved that the mixed Poisson distributions are appropriate choice in the process of modeling of the afore mentioned tariff system. The main result of the study is the construction of bonus-malus system based on mixed Poisson models, where expected value principle is used to determine the net premium. According to the analysis, it has been concluded that during the creation of a bonus-malus system in practice it is important to use certain mathematical and statistical models, as well as that the existing tariff system of automobile liability insurance in Serbia can be improved by introducing additional assumptions

Estimating the effect of a change in insurance pricing regime on accidents with endogenous mobility.

In this paper, we estimate the impact of introducing a bonus-malus system on the probability of having automobile accidents, taking into account contract duration or the client mobility between insurers. We show that the new incentive scheme reduces accident rates of all policyholders when contract duration is taken into account, but does not affect accident rates of movers that shirk the imposed incentive effects of the new insurance pricing scheme.Bonus-malus; contract duration; automobile accident; Poisson distribution; right- and left-censoring; exponential distribution.

Estimating the Effect of a Change in Insurance Pricing Regime on Accidents with Endogenous Mobility

In this paper, we estimate the impact of introducing a bonus-malus system on the probability of having automobile accidents, taking into account contract duration or the client mobility between insurers. We show that the new incentive scheme reduces accident rates of all policyholders when contract duration is taken into account, but does not affect accident rates of movers that shirk the imposed incentive effects of the new insurance pricing scheme.Bonus-malus, contract duration, automobile accident, Poisson distribution, right- and left-censoring, exponential distribution