A Study On The Pricing Method Of The Bonus-Malus System In Automobile Insurance

The automobile insurance which is also be called motor vehicle insurance is an important part of the market of non-life insurance.As the development of the social economy and the exaltation of the people's living standard,the automobile is more and more popular in China.And the automobile insurance is a kind of which has a large proportion in the non-life insurance of China.The premium income of the year 2009 in the non-life insurance of China has already been over seventy percent.The automobile insurance has become a competitive focus of the insurance market of China.So how to design a fair and reasonable rate of premium becomes the key of competition in the insurance market.Most of the insurance companies all around the world are using bonus-malus system to draw up the rate of premium of there automobile insurance which is short for BMS.The bonus-malus system is a kind of experience ratemaking method,the driver's renewable premiums is determined by his claim record in the past years.The insurer will charge more for the insurant who is at high risk.Instead they will charge less for the ones who is at low risk.The bonus-malus system in China is calle no claim discount which is short for NCD.Because the automobile insurance in China has only been started for a short time and the bonus-malus system is also not perfect,it becomes many problems:hunger for bonus behaviour,the inequity of the accumulative premium in a number of years and the inenquity of the premium which is paid by the insurants who have the same claim number but different amount of claim.The existence of these problems increases the operating risk of the insurers and impacts the development of the automobile insurance in a healthy way.Hence improving the existing bonus-malus system of China and solve the problems of it is an important task of making the existing bonus-malus system more fair and reasonable.There is three chapters in this paper:The Chapter One introduces the fundamental principle of the bonus-malus system of the automobile insurance.First it introduce the concept and functions of the automobile insurance which include the concept and features of the automobile insurance,the functions of the automobile insurance and the premium parts of the automobile insurance which is the base of the calculation method of the initial level premium in Chapter Two.Then I introduced the basic concept of the bonus-malus system of the automobile insurance.Fist it introduces the definition and the elements of the bonus-malus system of the automobile,then introduces the state transition matrix which is the basic model of the bonus-malus system of the automobile.Last is the probability distribution of steady state of the portfolio policy.After that it introduces the four main indexes to evaluate the the bonus-malus system of the automobile insurance:the relatively steady average level,the coefficient of variation of the premium the policy holder paid,the elasticity of the claim frequency about the relatively steady average level and the average optimal retention.In the end of this chapter it introduces the model theory of the optimal bonus-malus system which is the base of putting forward the models in Chapter Three.The Chapter Two is the calculation method of the initial level premium of the bonus-malus system of the automobile insurance. The initial level premium of the bonus-malus system of the automobile insurance is a part of the bonus-malus system of the automobile insurance,also the base of the pricing method of the bonus-malus system of the automobile insurance.Therefore In this chapter I write by the step of calculating the initial level premium,firstly I begin with the risk classification method,introduce the concept and features of the risk classification,then the six main selection standard of the risk classification variable:the fair standard,the feasibility standard,the management standard,the actuarial standard,the law standard and the morality standard.Then I list numbers of the staple risk classification variables from the risk factor of the automobile,the risk factor of the driver and the risk factor of the driving environment in detail.Thay are important considerable factors for the insurer to classify the new policy holder.Then I introduced the calculation model of the pure premium,give the staple models of the number of claim and the amount of claim from the calculation principle of the pure premium.The inusurer must condiser their own risk an the expense in management in the total premium,so they must add some proper additional amount from the pure premium.Hence I introduces some models of calculating the additional premium at the end of this chapter.As the core of this paper,in Chapter Three I put forward some method to improve the existing bonus-malus system of the automobile insurance.Firstly I begin this chapter with the problems and cause of the existing bonus-malus system of the automobile insurance and give some analysis of it,including the inequity of the accumulative premium in several years and the inenquity of the premium which is paid by the insurants who have the same claim number but different amount of claim.Then for the unequity of the total premium in several years of the exsiting bonus-malus system put forward the models of using the time series analysis method to determine the renewable premium.I give the introduction of the mathematic models of the time series analysis method in detail and the method of how to use the models.At last,I put forward the bonus-malus system considering both the times and the amount of the claim.Those models can solve the unequity of the policy holders who paid the same premiums with the same times of claim but different amount.With the introduction of the posterior distribution of the Inverse Gaussian structure funtion to be the base,I put forward the Poisson- Generalized Inverse Gaussian-Generalized Pareto Loss Model, the Poisson- Generalized Inverse Gaussian-Weibull Loss Model and the Poisson- Generalized Inverse Gaussian-Burr Loss Model.