Prediction Of Vehicle Insurance Claims Based On ARIMA-SVM Model

China's insurance market started and developed later than abroad,but after more than 20 years of development,it has gradually matured.In recent years,with the rapid economic development,insurance has been gradually divided into two major categories,life insurance and non-life insurance.As an important part of non-life insurance,motor vehicle insurance is also a relatively young insurance in non-life insurance,with great potential for development.With the increasing number of private cars,there are more and more people buying motor vehicle insurance.As owners of the purchased goods,they all want to buy a highly cost-effective motor vehicle insurance.For insurance companies that sell such products,they also want to set prices that can satisfy both their own profits and market competition.In the pricing of motor vehicle insurance,the historical experience of motor vehicle insurance claims and the prediction of future claims are all important pricing factors.For insurance companies,they can understand the trend of changes in the number of claims for motor vehicle insurance,and formulate relevant pricing strategies,setting a reasonable price as a guarantee for the company's revenue.There are also many studies on the number of claims for motor vehicles,and the distribution of traditional classic claims is one of them.This article also introduces the Poisson distribution,negative binomial distribution,and mixed Poisson distribution in the traditional classical claims number distribution.It also describes in detail the principles and steps of these types of distribution in the processing of claim number fitting,and also uses the moorings.The loose distribution,negative binomial distribution,and mixed Poisson distribution analyzed and predicted the number of motor vehicle claims from a branch of a property insurance company from 1997 to 2016,and found Poisson distribution,negative binomial distribution,and mixed moorings.When dealing with this type of problem,the loose distribution has a large mean absolute percentage error(MAPE)of the prediction results.The main reason for the analysis is the dependence on the law of large numbers and the lack of application of vertical historical experience.It only bases on a cross-sectional level.The number of motor vehicle insurance claims is a very complex nonlinear dynamic system that changes with time,so the sequence of claim times can also be viewed as a time series,as the ARIMA model for processing time series in the prediction of the number of claims.There should also be important applications.In this paper,the time series model is introduced in detail,including three aspects: The first is a detailed introduction to the mathematical principles of autoregressive model(AR),moving average model(MA)and autoregressive moving average model(ARIMA).Secondly,it is the introduction of the determination of each parameter in the ARIMA(p,d,q)model of the autoregressive moving average.Finally,it is an introduction to the modeling steps of the ARIMA model.After introducing the time series model,this paper applies the time series ARIMA model to analyze and predict the number of motor vehicle claims from a branch of a property insurance company from 1997 to 2016.The result shows that the time series ARIMA model predicts the number of claims.The effect is better than Poisson distribution,negative binomial distribution and mixed Poisson distribution,but there is still a larger mean absolute percentage error(MAPE)with the real value.The main reason for the analysis is that the ARIMA model deals with the smooth linear time series effect.Better,the non-linear part contained in the sequence of claims is not handled well.Although the time series ARIMA model has a good ability to handle a smooth linear time series(differential time series),the ARIMA model can also handle the linear part of the time series of motor vehicle claim times well,but the original claim number time series Both linear and nonlinear parts are included.Therefore,in the process of dealing with the original claims number time series fitting problem,it is also necessary to use other methods to deal with the problem of the nonlinear part of the time series,and extract the information of the non-linear part as much as possible.As a new small sample processing method,Support Vector Machine(SVM)has been greatly recognized.At the same time,support vector machine(SVM)is based on statistical learning theory and has good performance in dealing with small sample nonlinear problems,and it also has good generalization ability and generalization ability when seeking results at the global optimal solution level.Therefore,considering the advantages of both ARIMA and Support Vector Machine(SVM)in predicting the small sample data of the number of motor vehicle claims,this paper proposes a combination of ARIMA and Support Vector Machine(SVM)model to predict the problem.The number of claims is forecasted.Combining the idea of combination forecasting of motor vehicle insurance claims in this paper,this paper combines the advantages of ARIMA model and support vector machine(SVM)to establish an ARIMA-SVM combination forecasting model and modeling steps.Finally,the ARIMA-SVM combined forecasting model was used to analyze and predict the number of motor vehicle claims from a branch of a property insurance company from 1997 to 2016.The final empirical results show that the combination of the forecast model and the proposed number of claims The combined effect is indeed better than the single time series ARIMA model and the classical claim number distribution.Moreover,the ARIMA-SVM combined forecasting model not only overcomes the problem that the single ARIMA model has insufficient information extraction of the nonlinear part of the time series,but also avoids the number of classic claims.The distribution model laterally fits the problem of insufficient ability to handle tail risk data.This article is divided into seven chapters.The contents of each chapter are related to each other,but they all have their own main points:The first chapter gives an overview of the research background and significance of this article.It focuses on the research objects and methods of this article,and presents the research ideas and chapter arrangements of this article through the introduction of various treatment methods for the research objects at home and abroad.The second chapter gives a detailed introduction to motor vehicle insurance,mainly including the concepts and characteristics of motor vehicle insurance,and the main factors that cause these characteristics.It is precisely the complexity of these characteristics that also leads to the subsequent empirical process of the number of claims.Chapter 3 deals with the analysis of the number of claims and the follow-up model,so it gives a detailed introduction to the distribution of the number of traditional classic claims,mainly including the number of claims,the distribution of several classic claims: Poisson distribution,binomial Distributions,negative binomial distributions,and mixed Poisson distributions,etc.,and the mathematical principles of these types of distributions are described in detail in this chapter.Chapter 4 Considering the time series nature of the number of motor vehicle claims,consider using the classic time series ARIMA model for prediction.Therefore,the fourth chapter introduces ARIMA model in detail,including auto-regressive model(AR),moving average model(MA)and auto-regressive moving average model model(ARIMA)and analyzed the principle and parameter determination of each model,and finally introduced and explained the modeling steps and flow in time series forecasting.Chapter 5 gives a comprehensive introduction to Support Vector Machines(SVM).Firstly,it introduces the theoretical basis of statistical learning,generalization of the world,VC dimension,ERM(Minimization of Empirical Risk)and structural SRM(structural risk minimization criteria);Secondly,it gives a detailed introduction to the basic ideas,advantages,and kernel functions of support vector machines(SVMs);then,the related principles are developed for the two major aspects of support vector machine(SVM)classification and regression.Detailed description of mathematical expressions and practical applications;Finally,the combined principle of support vector machine(SVM)and time series ARIMA models is also analyzed,and the related modeling process and steps are also reflected.Chapter 6,firstly,this paper empirically analyzes the empirical data through the distribution of several classic claims,single ARIMA model and ARIMA-SVM combined forecast model,and then compares the distribution of each distribution model with the mean absolute percentage error(MAPE)value.effect.Finally,through empirical analysis,the corresponding empirical conclusions have been drawn.According to the data of small number of claims,the traditional classical claims number distribution fitting effect is not good,especially in the fitting of tail risk data error.This type of data with time-series properties,using the ARIMA model to predict its effect is better than the distribution of the number of traditional claims.However,the general time series ARIMA model only has good processing power for the stationary linear time series(differential time series),while the nonlinear part of the original time series needs to be processed by other methods.In this paper,the nonlinear support vector machine-Radial basis kernel function support vector regression is one of the good methods to deal with its nonlinear part.The empirical results in the radial basis ARIMA-SVM model also illustrate its ability to deal with such problems.Chapter 7 summarizes the work done by the paper and proposes further issues to be solved during the prediction of the number of motor vehicle claims.