Research On IBNR Based On The Generalized Linear Model

In recent years, as a result of China's great economic growth, non-life insurance market in China has developed rapidly. Non-life insurance business is often a "long tail". In other words, the period from claim to payment often cost a long time that can't be ignored. Therefore, it is necessary to establish loss reserving system. The loss reserving is the most important liability of non-life insurance companies on the balance sheet. But the loss reserving has great uncertainty. It's very difficult to set up a unified, precise mathematical model to estimate the amount of the loss reserving. What's more, the accuracy of loss reserving has a significant impact on the company's financial accounting and the company's solvency. Therefore, the insurance companies, policy holders and the CIRC has paid close attention to the loss reserving. China's "non-life insurance companies operating reserve management (for trial implementation)" in ArticleⅩⅢdefines four commonly used methods for loss reserving. They are the chain ladder method, the reserve development method, the payments per claim incurred method, and B-F method. These methods are based on the Run-off triangle. Then use formulas to determine the number of the loss reserving. These methods have their own different features, and the historical data are also different. However, these methods are some disadvantages. So the author will introduce the generalized linear model to evaluate the loss reserving.This paper includes the usage of actuarial, mathematical modeling knowledge, using comparative analysis, qualitative analysis and quantitative analysis method, to study the generalized linear model in the loss reserving evaluation.This paper is divided into five chapters.The first chapter, Introduction. This study focuses on the purpose and significance, research content, research innovation and inadequate.ChapterⅡ, the existing loss reserving estimation methods. First of all, it introduces the methods and principles of the chain ladder method, the reserve development method, the payments per claim incurred method, and B-F method. Then the author compares the four methods, and summarize the advantages of various methods, as well as the shortcomings.ChapterⅢ, generalized linear model theory. This chapter introduces generalized linear model to estimate the loss reserving. This chapter firstly discusses the generalized linear model's theoretical basis. This part focuses on the exponential distribution family, dummy variable and link function. These features make generalized linear model in estimating loss reserving more useful. Secondly, the generalized linear model commonly used statistical tests is summarized. Finally, a generalized linear model for the loss reserving is established.ChapterⅣ, the empirical analysis for loss reserving estimation. This chapter is the core of this dissertation. This chapter uses the current methods and generalized linear model to estimate the loss reserving. Then, the results of various methods are compared. The results show that the generalized linear model can be a good method of the loss reserving estimation. Comparing with the chain ladder method and the payments per claim incurred method, generalized linear model is more stable. Finally, the distribution of generalized linear model's selection problem is discussed.ChapterⅤ, the further expansion of generalized linear model. In the company's loss reserving evaluation process, more factors are considered. It is often difficult to describe these factors quantitatively. Therefore, the author uses the generalized linear model dummy variable to build a new model to estimate the loss reserving. This chapter introduces the company's claims policy variable, which expands the original generalized linear model, then makes empirical analysis.The innovations of this thesis are as follows(1)The thesis compares the generalized linear model with the current methods, pointing out the advantages and disadvantages of the generalized linear model.(2)The thesis introduces more external information to the generalized linear model. It makes the generalized linear model more practical.