The Bonus-Malus System Based On Claim Number And Claim Amount

Bonus-malus system is widely used in motor vehicle insurance which adjusts the pre-mium by the posterior information. That is to say, the insurer adjusts the premium of thefollowing year according to the claim record of policy-holder in that year using posteriorvariables.Consequently the premium that policy-holders pay is in proportion to their risk.However the common bonus-malus system only punish claim number,without consideringclaim amount,which is obviously unfair to the policy-holder that happen small claim forcompensation. At the same time,as the claim number is count data, poisson regressionmodel can’t fit it well for its characteristics of zero inflation and over-dispersion.Aim at the above problems and based on the former research,firstly this article selectsthe revision of the generalized zero inflation poisson model to fit the claim frequency accord-ing to its characteristics of zero inflation and over-dispersion; secondly, adds the penalty fac-tor of claim amount and analysis the transition rule of bonus-malus system with the methodof markov chain; finally, adopts geometric rate scale to calculate the tariff level.The main conclusion of this paper are: the modified generalized zero inflation poissonregression model can better fit the claim frequency for its characteristics of zero inflationand over-dispersion; the bonus-malus system based on the claim number and claimamount can better reflect the real risk of policy-holder; the geometric rate scale makes upfor the weakness of insufficient penalty to high-risk policy-holder and insufficient rewardto low risk policy-holder,which makes the collection of premium tend to be more reasonable.