Study On The Severity Of New Bonus Malus System In China

Bonus-Malus system(BMS)in automobile insurance is an actuarial model of rate estimation based on the historical loss experience of the insured.It is an important component of insurance pricing.To some extent,scientific and reasonable BMS not only relate to interests of the insured,but also reflect the insurance company's ability of predicting and evaluating risks.Therefore,it is a significant research to evaluate Bonus-Malus systems in automobile insurance comprehensively.This is one important subject of the actuarial science too.Based on the existing evaluation systems in automobile insurance,the main content of this paper is to compare the severity of Bonus-Malus systems adopted by China in 2007 and 2015,with the help of four non-classical evaluation indexes such as De Pril efficiency,relative average premium level,variation coefficient and adequacy of BMS.The improvement on severity of BMS adopted in 2015 is pointed out.The conclusions of these four indexes enrich evaluation contents of BMS,and achieve multi-angle,multifaceted comprehensive analysis of severity on BMS in 2015,in order to evaluate it from aspects of fairness,effectiveness,risk identification effect.The results are listed as follows:1.In the view of practice,policyholder pay close attention to the elements such as discounted value of the premium and the claim amount,the initial level of BMS.So,De Pril efficiency is introduced to evaluate the BMS.A practical calculation formula of De Pril efficiency is listed in third chapter.De Pril efficiencies of 2007'and 2015'BMS are calculated.The results for different risk levels,insurance times and initial levels are compared.Furthermore,De Pril efficiency for whole policyholders is also calculated by use of the results on different risk levels.2.When studying the steady-state distributions of BMS,it is found that the system needs long time to reach the stable state.Therefore,before reaching the steady state,the severity of BMS can't be evaluated by the common indexes for steady state accurately.In fourth chapter,the severity of 2007's and 2015's BMS are compared by use of the relative premium level and coefficient of variation in the finite time.It can be found that the evaluation result in the finite time is different from the one in steady state.3.In order to detect the consistency of theoretical risk and actual risk level in BMS,the adequacy of BMS is studied in the fifth chapter.The adequacy indexes of 2007's and 2015's BMS are calculated separately under the guarantee of financial balance.The results show that the 2015's BMS is better than the 2007's.