An Application Of Generalized Linear Model To Automobile Insurance Pricing

Automobile insurance plays an important part in the non-life insurance business, and its total premium income in the rate of property insurance has been reached 60% in recent years. Its development and changes have a huge impact on the entire non-life insurance market. After automobile traffic accident liability mandatory insurance has been implemented on July 1, 2006, China's automobile insurance market has presented several good features, such as fast growing in business, expanding in business coverage, the improvement of market order. These features will be the promotion of automobile insurance. However, the existing automobile insurance rate system can not meet the current development of the market economy, Automobile insurance premium rate does not reflect the real risk situation and can not conducive to the stability of the insurance companies.The State Council launched a comprehensive automobile insurance reform in the national on January 1, 2003. From January 1, 2003 on, China Insurance Regulatory Commission will no longer formulate the unified automobile insurance rate. Company can independently revise and adjust rates. This reform indicated the starting that the companies get the power of making the rate.At present, there are many methods and models in automobile insurance pricing, such as single-parameter analysis, minimum bias procedures, multiple regressions, Decision Tree, Neural Networks, Data Mining. Every method has its own advantages and shortcomings. This paper is based on the principles of classification pricing. After the comparison between the current classification rating (single-parameter analysis, minimum bias procedures, multiple regressions) and generalized linear models, it concludes the advantage of generalized linear models. The core content of this paper is discussing the automobile insurance rate using generalized linear models, and is giving a certain degree of guidance to other non-life insurance which meets the conditions of generalized linear models.The paper is using automobile insurance pricing as the main line. Based on the analysis of risk factors and the selection of risk classification variables, it also explores the pricing process of generalized linear models in automobile insurance. At last, the writer proposes the corresponding views to automobile insurance pricing.This paper is divided into five chapters.The first chapter is the introduction. At first, it describes the title of research background and the development trends in domestic and foreign research, as well as the research methods and innovation in this paper. According to the ratio of automobile insurance in non-life insurance business, it plays an important part in the non-life insurance business. Generalized linear model (GLM) has an earlier research abroad. It developed from linear model and based on the exponential family of distribution. While retaining a lot of the conventional thinking of normal linear regression model, it can analyze data which belong to non-normal distribution. Today generalized linear model is widely recognized as the industry standard method for pricing private passenger auto and other personal lines and small commercial lines insurance in the European Union and many other markets. This paper uses three research methods a combination analysis of qualitative and quantitative, comparative analysis and empirical analysis.The second chapter mainly explores the automobile insurance rate. This part starts from the concept and characteristics of automobile insurance, then analyses risk factor from the three aspects (automobile, driver, and environmental factors),concluding that automobile type, automobile use, automobile age, mileage, manufacturer, traffic region, the driver age, sex, marital status, occupation, driving experience, incident record,geographical and social environment have an important impact on accident rate and loss extent. These factors should be considered in pricing.The third chapter analyzes classification pricing. Risk classification variable is an important concept, not all of risk factors can be used as the risk classification variables. First of all, this chapter starts from discussing of the choice of variable of risk classification from the four points:the actuarial standards,management standards, social standards and legal standards, then analyze the drawbacks of the current method of classification pricing (single-parameter analysis, minimum bias procedures and multiple linear regression). After comparing all the three methods with generalized linear models, we can get the superiority of the use of generalized linear Model for pricing.The fourth chapter discusses the generalized linear model (GLM) and the score-pricing system. At first, the writer analyzes a class of special distribution-- the exponential family of distribution which meets the data characteristics of generalized linear model base on the comprehensive introduction of the basic principle of generalized linear model. Then link the loss of distribution and the distribution of exponential family by inversing the common loss distribution in non-life insurance as normal distribution, Poisson distribution and Gamma distribution into the distribution of exponential family. This is one of the innovations of this paper. At last, we get the score-pricing system and its applications through the comparison of the way of premium presentment and make the combination between the score-pricing system and the generalized linear models, which is another innovation of this article.The fifth chapter is the empirical analysis of the application of pricing in automobile insurance. First of all, the writer provides a pricing process of automobile insurance, including: the pricing factor analysis, data collection and collation, single-factor analysis, with the choice of risk variables and model, GLM analysis, the evaluation of the model, and so on. Finally, the paper takes empirical analysis of the data of third party liability insurance.