Research On Auto Insurance Rate Determination Based On Bootstrap Method

Since 2000,with the rapid development of China's economy and the increase in per capita disposable income,the per capita possession of automobiles has increased at a relatively rapid rate.At the same time,the entire automobile insurance market has been comprehensively developed due to the support of relevant national policies.Although the domestic insurance industry has developed late,after several decades of efforts by relevant personnel,the calculation method of motor vehicle insurance rates has been greatly improved,and the accuracy of the rate level has also been correspondingly improved.After the insurance companies have experienced the relatively rough pricing methods in the past,the current mainstream auto insurance rate pricing method is based on the generalized linear model.With the expansion of the insurance market,the generalized linear model still has a large advantage in the motor vehicle insurance rate determination method,but the disadvantages of the generalized linear model gradually emerge with the expansion of the auto insurance scale,such as the hypothetical provisions of the model.The influence of the covariate is a linear form of the prediction function,and it is assumed that the risk grading variables remain independent.These assumptions are not very consistent with the specific circumstances in the insurance actual business.If the linear estimation is simply used,some risk grading variables will lose important influence factors because they are not significant enough,and the correlation between risk grading variables cannot be accurately analyzed.In order to better adapt to the development of the insurance market and calculate more accurate insurance rates,relevant researchers need to further optimize the generalized linear model,so the random effects are introduced into the generalized linear model.To the generalized mixed model.Among them,the random effect can analyze the correlation between risk grading variables.Therefore,the generalized linear mixed model can analyze the influence degree of each risk grading variable on the response variable function from two aspects of fixed effect and random effect,and can also better analyze increasingly complex auto insurance claim data for future auto insurance premiums.The study of rate pricing methods provides a new way of thinking.In the model estimation method,the generalized linear model involves high calculus,so it is generally necessary to use the maximum likelihood estimation method for estimation.The traditional estimation method of the generalized linear mixed model is the penalty quasi-likelihood estimation method,which is relatively simple.It is currently the most widely used,but it is not accurate enough to use the penalty quasi-likelihood estimation method,especially the estimation of model parameters with small mean or large variance is biased.This paper introduces the Bootstrap method.For the analysis of a specific problem,the Bootstrap method is based on the problem itself.It only takes the observation data obtained and randomly samples it to get the closest parameter estimation without adding any Other artificial assumptions.In contrast,the traditional method tends to choose a hypothetical standard distribution model that enables the problem to be solved theoretically.This is not applicable in many practical situations,so the Bootstrap method will be more practical.Therefore,the research on the Bootstrap method can provide a reference for the estimation of model parameters.This thesis will use the disciplines of actuarial science and statistics as the theoretical support,using qualitative and quantitative,comparative analysis methods and the combination of theoretical research and empirical research,how to apply the generalized linear mixed model and Bootstrap method to the determination of motor vehicle insurance rates.Research is carried out in the process.The paper firstly introduces the development of the motor vehicle insurance market,the related role of the insurance,and the principles and influencing factors that need to be considered in the process of rate determination.The introduction of these basic theories is conducive to understanding the content of empirical analysis.After that,we briefly describe the traditional rate determination methods,such as the single-item analysis method and the minimum deviation method.The shortcomings of these methods force the insurance companies to use more generalized linear models.However,as the market scale expands,the generalized linear models are gradually difficult to meet.The actual situation needs,and then the generalized linear mixed model is studied.The original parameter estimation methods of generalized linear model and generalized linear mixed model have some deviations from the estimation results of auto insurance claim data.The introduction of Bootstrap method can effectively solve this problem.Therefore,the content of the empirical analysis includes two parts.One is to verify the applicability of the Bootstrap method for the determination of auto insurance rates,and the other is to verify that the parameter estimation result of the generalized linear mixed model under the Bootstrap method is Better than the generalized linear model.It can be seen from the concrete empirical results that the results of simulation experiments using random data show that the Bootstrap method is indistinguishable from the traditional method in estimating the model parameters,but when combined with actual data,it is found in the model.The Bootstrap method is superior to the traditional method in parameter estimation.At the same time,the empirical results show that the parameter estimation of generalized linear mixed model under Bootstrap method and traditional estimation method is better than that of generalized linear model.Finally,the specific calculation formula of pure premium based on Bootstrap method is obtained.