Evaluation And Empirical Analysis Of Outstanding Claims Reserve Based On GAMLSS

The reserve of non-life insurance business is the amount of money that a non-life insurance company needs to make in order to fulfill its policy liability,it can also be understood as a financial measure by which a non-life insurance company has unfulfilled responsibility for the policy.The insurance industry is a debt-operated industry,the reserve is the most important liability of a non-life insurance corporation,its accurate assessment will affect the company's solvency,the calculation of the company's accounting costs and the company's market competitiveness,it is of great significance to whether the company can operate stably.Because the rationality and adequacy of the withdrawal of the reserve will affect the company's operating conditions,its supervision is also one of the measures for the insurance regulator to measure the company's operations,it is also a necessary means to maintain market stability and has always been insurance.So it becomes a key point of concern for regulators.Therefore,the accurate assessment of reserves is one of the key issues to be solved by non-life insurance actuarial calculations.The research on its evaluation methods is also of great significance.Since the outstanding claims reserve is the amount to be paid in the future,it will be affected by many factors which are unsure,so its accurate assessment has always been difficult.There are many studies on the evaluation method of the outstanding claims reserve,when the evaluation method is divided,a common situation is to divide it into a deterministic method and a random method.Deterministic methods include the commonly used chain ladder method,B-F method,etc.The deterministic method is simple and intuitive,and can give a predicted value of the outstanding claims reserve,but the deterministic method cannot perform statistical tests on the obtained outstanding claims reserve,so the random method is gradually used for the assessment of outstanding claims reserve.The stochastic method is extended on the basis of the traditional method for evaluating the outstanding claims reserve,compared with the deterministic method which only obtains the point estimate,the random method can also perform statistical tests on the results of the evaluation.The generalized linear model,one of the important random models,covers a wide range of applications and is often used in the assessment of outstanding claims reserves.However,the generalized linear model also has certain limitations.For example,the distribution of response variables obeys the exponential distribution,and only the mean value can be modeled.Therefore,based on the generalized linear model,GAMLSS has been proposed by some scholars and applied in some fields,reactions variables of GAMLSS are no longer limited to exponential distribution families,it can be applied to more distribution types,and they can not only model the mean,but also consider parameters such as variance into the model.Based on the results of some literature studies at home and abroad,this paper expounds the importance of the evaluation of outstanding claims reserve and some traditional evaluation methods,which leads to the generalized linear model in the stochastic method,and proposes GAMLSS on the shortcomings of the generalized linear model.The two models were introduced and compared,and then the relevant knowledge was used to establish the model and analyze it in the empirical analysis.It was found that GAMLSS performed better than the generalized linear model in terms of model fitting and stability.There are five chapters of the text to discuss:The first chapter is the introduction.Firstly,it introduces the current status of the insurance industry and its future development trends,and points out that the development of insurance actuarial technology is also crucial.Then the concept of the outstanding claims reserve is briefly described,and the analysis of the outstanding claims reserve has a great impact on the management of the insurance company and the management of the insurance regulatory agency.Then a simple explanation is given on the evaluation method of the outstanding claims reserve,and several classification methods are summarized,and the classification of the deterministic method and the random method is emphasized.The following summarizes the status of the evaluation of outstanding claims reserve and the related model research at home and abroad,and it expounds the purpose of this study and the overall framework of the article.The second chapter is an introduction to some assessment methods for outstanding claims reserve of non-life insurance.The evaluation method is described one by one according to the classification method of deterministic method and random method.The deterministic method introduced includes chain ladder method,B-F method and Cap-Cod method,but the deterministic method can only get the point estimates for outstanding claims reserve,and the random method can perform statistical tests on the results of the evaluation.The random method introduces the Mack model and the lognormal model.It mainly describes the basic concepts and parameter estimation of the generalized linear model in detail,which is used as the preliminary knowledge of GAMLSS.The links and comparisons between the methods are described in the introduction of the evaluation methods in this chapter,and the advantages and disadvantages of the evaluation methods for outstanding claims reserve are summarized.The third chapter is a detailed introduction to GAMLSS.Based on the previous theoretical knowledge of generalized linear models,GAMLSS is introduced from the extension of distribution family and multi-parameter modeling.The theoretical knowledge is described in detail,and a distribution type that does not belong to exponential distribution is introduced——GB2 distribution,and the establishment of GAMLSS involving position and scale parameters for the evaluation of outstanding claims reserves,and on this basis,explores whether the calendar year effect has an impact on the model.Then introduces the parameter estimation methods of two commonly used models and their comparisons,and proposes the advantages and disadvantages of the goodness of the evaluation model that can be used by AIC,SBC and other indicators.At the end of this chapter,GAMLSS was evaluated.The fourth chapter is empirical analysis.The data is selected from the compensation data of the commercial vehicle business in Shi(2011).The generalized linear model and GAMLSS are respectively established for the data.The analysis is between the generalized linear model and GAMLSS under the Gamma distribution,in which GAMLSS simultaneously models with location and scale parameters,the GAMLSS's fitting effect is better;for GAMMSS under Gamma distribution and GB2 distribution,GAMLSS under GB2 distribution is better than Gamma for the data of the group with the increase of modeling parameters and the extension of the distribution range.And after joining the calendar year,you can observe that the fitting effect of the model has been improved,and the effect of the calendar year has an impact on the evaluation.Finally,the sensitivity test of GAMLSS shows that the stability of GAMLSS is better than that of generalized linear model.The fifth chapter is the conclusion.First of all,combined with the previous method comparison and empirical analysis,make a summary of the content of the article discussion,summed up the application of GAMLSS in the evaluation of the outstanding claims reserve is still relatively good,using GAMLSS to assess the outstanding claims reserve is still better.Finally,the shortcomings in the analysis process are discussed,and the areas where the article can be improved and the direction of continuing research are pointed out.In response to the above conclusions,in the last section of this chapter I also select the indemnity data of an insurance company in China,and use the same method to carry out verification analysis,and finally draw a consistent conclusion.At present,most of the research on GAMLSS is in the determination of auto insurance pricing rate,and there are fewer applications in the reserve evaluation,there is even less detailed comparison between GAMLSS and generalized linear model.The innovation of this paper is comparing and analyzing GAMLSS and generalized linear models from various aspects,and exploring the impact of calendar year on the model.