Research On Classification Ratemaking Of Automobile Insurance Based On Generalized Linear Models

Taking first and being the largest among non-life insurance sectors, the profitability of the automobile insurance industry plays a decisive role in the operational efficiency of insurance companies. Generally, the automobile industry does not function well in China, because the insurance provider’s loss ratio on settlements has exceeded50%for most years. The excessive high settlements in the automobile insurance industry present two problems:first is the unreasonable premium rate, and the other is that the risk of loss lacks adequate control. The former cannot be simply expressed as the rate being too high or too low. Instead, the issue lies in that the current policy makes no distinction in rate scales between the types of vehicles covered, i.e., non-luxury vs. luxury. This generates greater instances of adverse selection leading to poor insurance company quality and an unbalanced relationship between premium income and the risk being covered. Meanwhile, the unjustifiably high payout to premium ratio shows that insurance companies lack a proper understanding of the risk and thus cannot quantify and predict the risk being insured against. They cannot effectively control the risk. An unclear method of pricing premium rates and a system that is too general in matching rates to types of vehicles covered means that insurance companies set themselves up to carry a heavy burden further down the road. Because of this imbalance in the system, insurance providers are urgently seeking a more effective method to control risks. The actuarial study about pricing premium insurance becomes a primary point of breakthrough.The generalized linear models can be formally seen as a promotion of the classic linear model. The classic linear regression model is built on the basis of symmetric normal distribution and assumes that variance is a constant value. In practice however, insurance data often displays very a numerical variance trend. For example, variable distribution such as claim intensity tends to have a heavy right tail, and the dependent variable is no longer confined to the linear dependence of the explanatory variables. The assumption of normal distribution from the dependent variable in the classic linear model has been relaxed for dispersion parameters of exponential family of distribution in generalized linear models. The generalized linear model links the linear combinations of the independent variables with the variance of dependent variable through copulas. This provides possibility for fitting a specific interval (claim intensity is a non-negative). It also meets the more complex non-linear relationship between some dependent variables and independent variables in the practical application. Hence, it overcomes the limitation on the application of the classical linear model.In this paper, we will try to use the generalized linear models to study the rate-making classifications of the automobile insurance industry in China. This paper is divided into six chapters. The first chapter describes the background and significance of the study, investigates related and relevant source materials at home and abroad, and presents research content, methods, ideas, as well as innovation and deficiencies. The second and third chapters will present the theoretical basis of this article. Risk classification is the basis of rate-making classification in the automobile industry. Improper classification will affect the accuracy of determining the premium rate. So the second chapter focuses on the theory of risk classification, including the selection of risk factors and classification variables, and the methods of risk classification. The third chapter introduces the classification ratemaking model of automobile insurance and consists of one-way analysis, iteration method, and generalized linear models. It discusses the advantages of generalized linear models compared with other models from aspects of the applicability of insurance data, the integrity of the statistical framework, and simple operation of the software. The fourth and fifth chapters carry the emphasis of the full article. The fourth chapter systematically states the process of using generalized linear models to explore the automobile insurance industry and summarizes the methods of each step and problems that claim attention. It provides guidance for the next chapter’s empirical analysis. The fifth chapter is the empirical section of the article. The data source is a selection of public liability insurance loss data. This section builds generalized linear models analyzing the number of claims and claim intensity respectively. As for the problem that the coefficient of the model is not significant, we try to adopt the merger level of risk to form a new risk category and to build a related model again. The empirical results find that a generalized linear models about the number of claims fits best under the assumption of a negative binomial distribution, while the claim intensity does not behave well under the gamma distribution. The sixth chapter is the conclusion. It analyzes the difficulty of the generalized linear models and the problems that need attention.