| Bonus-Malus System,also called No-Claim Discount,is an important part of price for automobile insurance,used widely around the globe.On one hand it encourages the insureds to drive safely,on the other hand it distinguishes the underlying risk of the insureds by increasing renewal premium for the insureds who have claimed and decreasing renewal premium for the insureds who have no claims.From the perspective of auto insurance pricing,the purpose of BMS is to allocate the cost burden of policies portfolios fairly to every insured according to his underlying risk.Along with the revival reform of the clause and rate marketing of commercial automobile insurance in China in 2015,Insurance Association of China have released a new version of BMS.Both the number of bonus-malus levels and the spectrum of relativities have risen in this version.This generates a lot of media attention,and it is interpreted that the premiums of the major insureds will be decreased.And the difference of premiums between"good driver" and "bad driver" will be enlarged in this new version of BMS.Is it true?And is it consistent with the goal of BMS?If not,what can we do?The work in this thesis mainly focuses on these issues with actuarial perspective.The full text is divided into seven chapters.The first chapter is an introduction of this thesis.Firstly,the research background and significance is introduced by the reform of the clause and rate marketing of commercial automobile insurance in China in 2015.Secondly,the research angle and routine is determined based on the literature review of domestic and international BMS research.The main context and innovations is outlined in the end of this chapter.The second chapter is theoretical basis.Firstly,the process of automobile insurance rating,the position of BMS,and the interaction of prior rating and BMS are clarified.Secondly,the tools of evaluation and design of BMS are summarized.In the third chapter,we firstly introduced the fact of automobile insurance rating after the reform of the clause and rate marketing of commercial automobile insurance in China in 2015.Then we compared the severity of' punishment and the efficiency of transition rule of the new version of BMS with the old version of BMS,and the results show the severity of punishment has raised,while the efficiency of transition rule has declined.In addition,the transition rule itself has defect,it seems to punish the good driver and protect the bad driver in the long run.In the end of this chapter,we did an empirical test of the problem of over penalty and rewards used the claims data of domestic property insurance company with the actual bonus-malus system in China,the result indicates the problem of over penalty and rewards exists indeed in real word,and it becomes severe along with the number of BMS levels.The fourth chapter is the core of this thesis.We try to handle the problem of over penalty and rewards by varying transition rule.Secondly we introduced three types of varying transition rule:risk-varying,level-varying and general varying.and then we compared their efficiency of these transition rules with different data,different prior rating processes and different number of BMS levels,the results all proof that risk-varying transition rule is the most efficient type.The fifth chapter interpreted the computation of the relative premium of optimal BMS.In this chapter,the relative premiums of nationwide version(excluding BeiJing and XiaMen)of BMS has been computed with risk-varying transition rule combined the domestic property insurance company claims data based on the concept of relative premium of optimal BMS under constrained financial equilibrium and unconstrained financial equilibrium.Furthermore,we compared the ability of optimal BMS with risk-varying transition rule to help relieve the severity of over penalty and rewards with the optimal BMS corresponding simple transition rules.And the results show the ability of the optimal BMS with risk-varying transition rule is higher.The relative premiums of Bei Jing,XiaMen version of BMS has developed with two different methods of risk-varying transition rule.We found that the efficiency of transition rule can not be the only criterion in the selection of transition rule,the expect of prior claims frequency of different BMS levels must be referred to.The sixth chapter discuss the linear relative premium of optimal BMS.The linear relative premium is improvement of the relative premium in the former chapter for business application.Firstly,the background and computation of the linear relative premium is introduced.Secondly,the linear relative premiums of nationwide version(excluding Beijing and Xiamen)and Beijing,Xiamen version of optimal BMS has been computed with the risk-varying transition rule based on the claims data of domestic property insurance company.The empirical analysis showed the linear relative premium is more regular than the bayes relative premium in the former chapter,and the loss of forecast accuracy is little.The seventh chapter has made a summary discussion of the full text and given some suggestions for future BMS design.In the end,we proposed some study directions about BMS in the future.The main innovations in this thesis concludes:Firstly,we have evaluated the rationality and fairness of the new version of BMS in China;Secondly,we have done empirical analysis of over penalty and rewards in the design of optimal BMS when there are covariates with real data and real BMS in China;Thirdly,we have assessed the efficiency of varying transition rules with different data and different number of BMS levels.Fourthly,integrated with prior premium we developed two types of optimal BMS scales with varying transition rule based on the BMS numbers in China and evaluated its effect on the lessen of over penalty and rewards. |
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