基于Copula函数的非寿险多元索赔准备金评估方法的研究

发布时间：2018-01-03 15:43

本文关键词：基于Copula函数的非寿险多元索赔准备金评估方法的研究　出处：《沈阳工业大学》2016年硕士论文　论文类型：学位论文

【摘要】：非寿险索赔准备金评估方法是非寿险保险公司资产负债表中重要的一部分,也是中国保险监督管理协会对保险公司监管的评估手段。评估索赔准备金的方法可以分为一元索赔准备金评估方法和多元索赔准备金评估方法,一元索赔准备金评估方法是传统性方法,在实务操作中已经成为一种固定的体系,所以目前的研究均着重于多元索赔准备金评估方法上。而在概率论领域,解释多元相关性的一个比较实用的函数是Copula函数,其多用于金融股票领域,用于分析与估计不同股票的发展趋势或不同金融变量之间的相关性。本文基于以上背景,在多元索赔准备金评估方法上,对多元索赔准备金进展法和多元索赔准备金Munch链梯法进行改进。准备金进展法在确定性准备金进展法的基础上,加入变量的随机性因素,优化为随机性准备金进展法。本文在随机性准备金进展法的基础上,通过Copula函数估计具有随机性变量之间的相关性,将Copula函数独有的特征与准备金进展法相结合。同样的,链梯法也是传统的一元索赔准备金评估方法,其在前人的基础上,依次优化为了Munch链梯法、随机性Munch链梯法。本文首先使用非参数核密度的方法来估计变量之间的Copula函数,然后在随机性Munch链梯法的基础上,通过估计出的Copula函数来解释相关性,从而对随机性Munch链梯法进行优化改进。在实例分析部分,本文选择了在非寿险理论研究中具有代表性的累计已付赔款流量三角形与累计已报案赔款流量三角形进行数例分析。对于多元准备金进展法,分别计算与比较具有确定性的准备金进展法、具有随机性的准备金进展法与基于Copula函数的多元准备金进展法得出的索赔准备金的预测均方误差及其预测分布。类似地,对于多元Munch链梯法,比较Munch链梯法、具有随机性的Munch链梯法和多元Munch链梯法与Copula函数相结合所计算出的未决赔款准备金的预测分布与预测均方误差的大小。运用MATLAB数学软件和Bootstrap方法,比较结果可以看出,在预测均方误差的度量中,基于Copula函数的多元准备金进展法所得的值小于随机性准备金进展法所得值;基于Copula函数的多元Munch链梯法得出的值小于随机性Munich链梯法与Munich链梯法得出的值。这说明对Copula函数的引入是有效的。
[Abstract]:Non life insurance claim reserve evaluation method is a part of non life insurance companies in the balance sheet is also important, evaluation means China insurance supervision and Management Association of insurance company supervision. Evaluation method of claim reserve can be divided into one yuan claim reserve evaluation methods and the multiple claim reserve evaluation methods, a claim reserve evaluation method is a traditional element the method, in practice has become a fixed system, so the current research focuses on multiple claim reserve evaluation methods. In the field of probability theory, interpretation of a more practical function of multiple correlation is the Copula function, it is mostly used for financial stocks, for the analysis and estimation of the correlation between the development of the trend of different stocks or different financial variables. Based on the above background, the multiple claim reserve evaluation methods, the multiple claims of quasi Progress in the synthesis of gold method and multiple claims reserve Munch chain ladder method was improved. The reserve development method based on traditional reserve development method, adding random factors as random variables, the optimization of the reserve development method. In this paper, the random reserve development method, through the Copula function estimation is the correlation between random variables the feature and reserve development method Copula function unique combination. Also, evaluation methods of the chain ladder method is a traditional one yuan claim reserve in the previous basis, in order to optimize the Munch chain ladder method, random Munch chain ladder method. Firstly, using the method of non parametric kernel density estimation the Copula function between variables, then based on random Munch chain ladder method, Copula function through the estimated to explain the correlation, thus to optimize the randomness of the Munch in the chain ladder method. Part of case study, this paper chooses the total claims paid traffic triangle representative in the non life insurance in theoretical research and accumulated report claims triangular flow cases were counted for multivariate analysis. The reserve development method, calculate and reserve development method compared with the deterministic and stochastic reserve development method and prediction based on Copula function multiple reserve development obtained claims reserves mean square error and its distribution prediction. Similarly, the multiple Munch chain ladder method, Munch chain ladder method, the randomness of the Munch chain ladder method and multiple Munch chain ladder method and Copula function combining forecasting and prediction of distribution of outstanding claims reserve calculated by the the size of the square error. Using MATLAB mathematical software and Bootstrap method, the comparison results can be seen in the measurement of the mean square error of prediction, based on Copula function The multi reserve development method is less than the value of the random reserve development method; the Copula function of the chain ladder method of multiple Munch value is less than the random Munich chain ladder method and Munich method based on the value chain ladder. This shows that the introduction of the Copula function is effective.

【学位授予单位】：沈阳工业大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212

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