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Research on IBNR Based on the Generalized Linear Model

Author: ShiZhiCheng
Tutor: ZhangYunGang
School: Southwestern University of Finance and Economics
Course: Insurance
Keywords: Provision for outstanding claims Traffic Triangle Generalized Linear Models Poisson distribution Gamma distribution SAS
CLC: F224
Type: Master's thesis
Year: 2010
Downloads: 157
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Abstract

In recent years, as China's rapid economic development, increasing motor vehicle laws and regulations to gradually improve, the rapid development of China's non-life insurance market. Non-life insurance business tend to have \Outstanding claims reserve, also known as loss reserves (loss reserving), an insurance company for those in the accounting year end when the loss occurred but have not yet been closed by Pei for reparations, and it is non-life insurance on a company's balance sheet significant liabilities. But tend to have outstanding claims reserve great uncertainty, to establish a unified, accurate mathematical models to estimate the amount is quite difficult. The outstanding claims reserve accuracy of assessment of the company's financial accounting, objectively reflect the operating results and ensure that the company has a major impact on solvency, has been the insurance company, policy holders, CIRC focus objects. Our newly revised \And China's \and BF methods. These methods are based on the triangle as a data flow basis, using the formula established claim reserves. These methods have their own characteristics, the use of historical data to also different. But there are some limitations, such as can only be done on the outstanding claims reserve for point estimates and can not estimate the degree of fluctuation; fluctuations on empirical data is more sensitive and more. So I tried to introduce a generalized linear model, the outstanding claims reserve for evaluation. This article will use actuarial, mathematical modeling of the relevant knowledge, the use of comparative analysis, qualitative analysis and quantitative analysis method to study the generalized linear model in outstanding claims reserve evaluation of application problems. From the perspective of theoretical and empirical discussion of two generalized linear models in outstanding claims reserve Assessment and to make the evaluation results of its application. In order for the outstanding claims reserve assessment practices to provide reference and help. This thesis is divided into five chapters. The first chapter, Introduction. This study focuses on the purpose and significance of research contents, innovation and inadequate. Analysis of the current reserves for outstanding claims of the status quo, and pointed out the shortcomings of the study, propose to continue to claim reserves estimation methods research is very necessary. Chapter II, the current outstanding claims reserve estimation methods. Firstly, introduced the chain ladder method, the reserve progress, average payouts methods, and BF method calculation principle. Then starting from the principle of four methods summarized compare these four methods. Summarizes the use of various methods to historical information, as well as features and shortcomings. Illustrates the most commonly used method of claim reserves estimation, have their own characteristics, but there were insufficient use of historical data for reporting delay is more sensitive to the final loss ratio is very sensitive, and many other defects. Chapter III, generalized linear model theory. Analysis based on the second chapter, this chapter introduces the generalized linear model to estimate the provision for outstanding claims. Generalized linear models as an extension of ordinary linear regression has been introduced into the non-life insurance actuarial. However, generalized linear models in non-life insurance application rates are mostly confined to the hierarchical analysis, based on the outstanding claims reserve of very few. This chapter begins with a detailed discussion of the theoretical basis of generalized linear models. Focused on the exponential distribution family, dummy variables and connection functions, these three different aspects of ordinary linear regression. Exponential family generalized linear model makes the distribution of the dependent variable in the form of greatly Extension, not just confined to the normal distribution. This makes the generalized linear model to better fit the non-life business loss data, because these data tend to have a significant positive bias. The dummy variable is introduced, making it difficult to quantify factors can be reflected in the model. Connect the mean function of the dependent variable part linked with the linear, generalized linear model differs from ordinary linear regression using the unit connected to the function, the ability to define a richer connection function. These features make the generalized linear model in outstanding claims reserve estimates more advantages. Secondly, this chapter summarizes the generalized linear models commonly used statistical tests. Finally, the claim reserves established its corresponding generalized linear models. Taking into account the full use of the historical data, this paper respectively, and the average number of claims against the claims are forehead and a generalized linear model. Based on the experience of non-life insurance law loss occurs, the number of model selection Pei Poisson distribution, the average claim amount used Gamma distribution. Chapter IV, outstanding claims reserve estimates empirical analysis. This chapter is a full text of the core. First, the introduction of historical data, and the data do the initial processing. Collation of historical data traffic triangle form, so that data can be applied separately to the chain ladder method, the average payouts methods and generalized linear models. And, secondly, the use of methods currently used to estimate claim reserves. Then,. Using generalized linear models to estimate and compare the results of various methods. The results show that the generalized linear model can be well fitted estimate claim reserves. In the sensitivity tests, generalized linear model is better than the chain ladder method and the method of average claim amount is more stable. Empirical evidence from the perspective of the generalized linear model in outstanding claims reserve estimates advantage. Finally, the distribution of the generalized linear model selection problem to make discussion. Respectively, using the normal distribution, Gamma and inverse Gaussian distribution model for the average claim amount to fit. Found that the worst fit a normal distribution, also shows that the use of ordinary linear models to assess outstanding claims reserve is inappropriate. When the dependent variable when selecting a different distribution form the conclusion that the outstanding claims reserve relatively large difference between the estimated value. Therefore, I believe in the actual application process, select the distribution of the dependent variable when the form should be very cautious. And proposed distribution of the dependent variable in the selection form, we should not only be based on the merits of a certain value judgments, but should be combined with practical experience in many aspects to consider. Chapter V, generalized linear model assessment of outstanding claims reserve further application. In the company's actual outstanding claims reserve evaluation process, an impact on the results of the assessment of many factors. Progress is not just an accident years and years for outstanding claims reserve impact, including business structure, claims policy, climate and environment, laws and regulations and other factors. And these factors on the impact of outstanding claims reserve is often difficult to quantify. I will be using generalized linear models dummy variables of this feature, the company claims policy of this variable as an example of the generalized linear model can be extended to build a new model to estimate the provision for outstanding claims. This chapter first analyzes in addition to accidents, the progress beyond the influence of claim reserves and other factors. Then, the introduction of the company's claims policy variables, the original generalized linear model can be extended to finally make the empirical analysis to prove the feasibility of the model. I believe that the innovation of this paper is mainly manifested in: (a) the generalized linear model analysis and comparison with the existing advantages and disadvantages compared. This paper describes the use of empirical methods, generalized linear models, compared with the current method is far more stable. As for the choice of a model (including the distribution type, connection functions, etc.) was very sensitive. This requires us to build a model, combined with the actual claims experience choose carefully. (2) the introduction of more external information, makes the model internalize external variables. This paper introduces a new variable, making an already exist in the model external information is incorporated within the model. The model will be expanded company claims policy changes introduced into the model in the past, making an already require actuaries to estimate the impact of the use of experience can now be estimated using the model itself.

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