本文關(guān)鍵詞：基于Copula函數(shù)的非壽險多元索賠準備金評估方法的研究　出處：《沈陽工業(yè)大學》2016年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 多元準備進展法 多元Munch鏈梯法 Copula函數(shù) Bootstrap方法

【摘要】：非壽險索賠準備金評估方法是非壽險保險公司資產(chǎn)負債表中重要的一部分,也是中國保險監(jiān)督管理協(xié)會對保險公司監(jiān)管的評估手段。評估索賠準備金的方法可以分為一元索賠準備金評估方法和多元索賠準備金評估方法,一元索賠準備金評估方法是傳統(tǒng)性方法,在實務操作中已經(jīng)成為一種固定的體系,所以目前的研究均著重于多元索賠準備金評估方法上。而在概率論領(lǐng)域,解釋多元相關(guān)性的一個比較實用的函數(shù)是Copula函數(shù),其多用于金融股票領(lǐng)域,用于分析與估計不同股票的發(fā)展趨勢或不同金融變量之間的相關(guān)性。本文基于以上背景,在多元索賠準備金評估方法上,對多元索賠準備金進展法和多元索賠準備金Munch鏈梯法進行改進。準備金進展法在確定性準備金進展法的基礎(chǔ)上,加入變量的隨機性因素,優(yōu)化為隨機性準備金進展法。本文在隨機性準備金進展法的基礎(chǔ)上,通過Copula函數(shù)估計具有隨機性變量之間的相關(guān)性,將Copula函數(shù)獨有的特征與準備金進展法相結(jié)合。同樣的,鏈梯法也是傳統(tǒng)的一元索賠準備金評估方法,其在前人的基礎(chǔ)上,依次優(yōu)化為了Munch鏈梯法、隨機性Munch鏈梯法。本文首先使用非參數(shù)核密度的方法來估計變量之間的Copula函數(shù),然后在隨機性Munch鏈梯法的基礎(chǔ)上,通過估計出的Copula函數(shù)來解釋相關(guān)性,從而對隨機性Munch鏈梯法進行優(yōu)化改進。在實例分析部分,本文選擇了在非壽險理論研究中具有代表性的累計已付賠款流量三角形與累計已報案賠款流量三角形進行數(shù)例分析。對于多元準備金進展法,分別計算與比較具有確定性的準備金進展法、具有隨機性的準備金進展法與基于Copula函數(shù)的多元準備金進展法得出的索賠準備金的預測均方誤差及其預測分布。類似地,對于多元Munch鏈梯法,比較Munch鏈梯法、具有隨機性的Munch鏈梯法和多元Munch鏈梯法與Copula函數(shù)相結(jié)合所計算出的未決賠款準備金的預測分布與預測均方誤差的大小。運用MATLAB數(shù)學軟件和Bootstrap方法,比較結(jié)果可以看出,在預測均方誤差的度量中,基于Copula函數(shù)的多元準備金進展法所得的值小于隨機性準備金進展法所得值;基于Copula函數(shù)的多元Munch鏈梯法得出的值小于隨機性Munich鏈梯法與Munich鏈梯法得出的值。這說明對Copula函數(shù)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.

【學位授予單位】：沈陽工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O212

【相似文獻】

相關(guān)期刊論文 前10條

1 李健倫,方兆本,魯煒,李紅星;Copula方法與相依違約研究[J];運籌與管理;2005年03期

2 單國莉,陳東峰;一種確定最優(yōu)Copula的方法及應用[J];山東大學學報(理學版);2005年04期

3 羅俊鵬;;基于Copula的金融市場的相關(guān)結(jié)構(gòu)分析[J];統(tǒng)計與決策;2006年16期

4 李霞;曾霞;侯兵;;copula的構(gòu)造以及copula之間關(guān)系的研究[J];商丘師范學院學報;2006年05期

5 孫志賓;;混合Copula模型在中國股市的應用[J];數(shù)學的實踐與認識;2007年20期

6 李娟;戴洪德;劉全輝;;幾種Copula函數(shù)在滬深股市相關(guān)性建模中的應用[J];數(shù)學的實踐與認識;2007年24期

7 許建國;杜子平;;非參數(shù)Bernstein Copula理論及其相關(guān)性研究[J];工業(yè)技術(shù)經(jīng)濟;2009年04期

8 杜子平;閆鵬;張勇;;基于“藤”結(jié)構(gòu)的高維動態(tài)Copula的構(gòu)建[J];數(shù)學的實踐與認識;2009年10期

9 王s，

本文編號：1374553