Research On Distribution Model Of The Motor Vehicle Insurance Claim Frequencies

As the development of China’s automobile industry and people’s living standardsimprove,China’s civilian car ownership has been growing rapidly with an increase of16.4%compared to that of2010to reach105.78million at the end of2011.Make themotor vehicle insurance market which depend on auto stock market has much roomfor growth.In2010, the property insurance premium income reach to402.7billionyuan, of which motor vehicle insurance premium income reach to300.4billionyuan,accounting for74.5%of the property insurance premium income, increase of39%compared to2009.Motor vehicle insurance become an important pillar of theproperty insurance company.While China’s motor vehicle insurance business in the rapidly growing, alsofaces the risk of high loss ratio.This not only led to operating losses of the insuranceindustry, but threaten the solvency of insurance companies, not conducive to the riskcontrol of motor vehicle driving and management of road traffic safety.Therefore, thescientific pricing for motor vehicle insurance,so that each policyholder can pay thepremium to match with the actual risk, encourage insurant active control risks, reduceinsurance accident, lower the loss ratio.That’s China’s insurance industry achievehealth sustainable development facing the reality choice.Bonus-Malus System of motor vehicle insurance is an experience pricingmethod.Increase the insured’s premium or punish insurant who occur once or multipletimes claims record last year,give insurant a premium discount or reward who has noclaim record last year.In this pricing, the number of claims is the most importantfactor,it decided the motor vehicle insurance discount rates.Therefore, research on thedistribution of the number of claims to find the most reasonable fitting model, topredict future policy holders’ risk level and the number of claims,is of greatsignificance for the establishment of a scientific and reasonable bonus-malus system.This paper first describes the basic theory of motor vehicle insurance and the bonus-malus system of motor vehicle insurance, summarizes the actuarial research ofdomestic and foreign scholars involved in motor vehicle insurance claim frequencydistribution model.Secondly, summary and analysis of binomial distribution, Poissondistribution,negative binomial distribution, Poisson inverse Gaussian distribution，negative binomial beta distribution, binary risk model, the triple risk model, theexponential distribution class of mixed distribution.Given the probability densityfunction of them,study the nature and characteristics of these distributions,comparative and analysis the difference between these distributions.Then,introducethe GGD distribution parameter based on α, θ. Given and proved its probabilitydistribution function and probability density functional form. Research the nature ofthe GGD distribution on different parameters,Given the estimated parameterexpression research of GGD distribution,research the differences and relations withother distribution.Finally,use the actual number of claims data of insurance companiesto parameter estimation and data fitting with GGD distribution and other classicalnumber of claims distribution data fitting.Found that GGD distribution can get a goodfit for the number of motor vehicle insurance claims data,show the advantages of thisdistribution compared with other classical number of claims distribution.GGDdistribution is very suitable as the claims distribution of bonus-malus system toestablish a more reasonable optimal bonus-malus system.