Generalized Liner Models Based On Lasso Method And Its Application In Vehicle Insurance

With the rapid growth of China's auto industry and the increase of car ownership,the role of vehicle insurance rate in the field of non-life actuarial actuarial is becoming more and more important.At present,the generalized linear model(GLM)has an extremely wide range of applications in the non life actuarial field(especially the car insurance business).And compared with traditional rate determination method(single factor analysis method,minimum deviation method,multiple linear regression model,etc.),GLM has great progress in the theoretical basis,applicability,and diagnosis of the model.However,in actual modeling,GLM still has some shortcomings.For example,when modeling,GLM does not take account of multiple collinearity among variables and the over-fitting problem of models,which will affect the accuracy of model estimation.In 1996,Tibshirani,R.proposed a new method of variable selection,namely,the Lasso(Least absolute shrinkage and selection operator)method.The Lasso method can filter out the significant variables in the model and estimate the parameters of the corresponding variables.The combination of GLM and Lasso method can not only bring the advantage of GLM,but also handle the multicollinearity problem among model variables,and improve the accuracy and applicability of the model results.On the basis of the existing research results,this paper further combines the GLM with the Lasso method and applies it to the rate determination of vehicle insurance.The main tasks are as follows:Firstly,we analyze the development of China's car insurance market,expound the current vehicle insurance rate determination model and the domestic and foreign research status of Lasso regression,and explain the main contents and methods of this paper.Secondly,we combine the theory of GLM and Lasso regression,and the general solution algorithm of Lasso-GLM is expounded.Thirdly,introduce Lasso-GLM into vehicle insurance rate determination,and sum up the main steps of using Lasso-GLM to determine vehicle insurance premium rate.Fourthly,Apply Lasso-GLM to the rate determination of car insurance and compare with the results of GLM.The results showed that the Lasso-GLM's fitting effect was better for the data of this group.Finally,based on the results of comparative analysis,some policy recommendations are given in the light of the current situation of vehicle insurance market in China.