改进Bootstrap方法在未决赔款准备金估计中的应用

发布时间：2018-03-30 22:27

本文选题：未决赔款准备金　切入点：传统链梯法　出处：《吉林大学》2014年硕士论文

【摘要】：自改革开放以来,我国的保险业一直保持着一个快速发展进步的态势,获得了非常显著的成绩.但是我国的保险市场还处于初级发展阶段,起步晚,推进程度比较低,整体的发展水平相对比较滞后,需要面临的挑战很多.我国的保险公司要想在这个竞争强烈的大环境中,得到自己的一席生存之地,培养和提高核心竞争力是十分必要的.对于保险公司而言,开发竞争潜力的重要经营举措即为投资.在盈利的同时,为保证保险公司的正常运营,准备金的提取以及投资比率的决策,就显得尤为重要.保险公司的财务报表上一项十分重要的负债即为未决赔款准备金,它的计提比例影响到保险公司投资收益的多少和赔付能力的强弱.因此,对于准备金评估,有着重要的实际意义. 目前准备金提取应用最广泛的是确定性模型估计方法,例如链梯法(ChainLadder Method)、逐案估计法(Case-By-Case Estimating Method)、B-F方法、准备金进展法等等.然而这类办法虽然操作简单,模型易懂,但是受到很多随机因素的影响,估算精度并不高.近些年来,精算领域对准备金提取方法进行了很多相关的研究,利用了现代概率与数理统计的理论,将动态的随机模型应用到了准备金估计中去,如对数正态模型、Mack模型、广义线性模型、贝叶斯模型、Bootstrap方法等统计方法都引入到了准备金的预测中.本文在前人研究成果的基础上,引入了改进的Bootstrap方法在未决赔款准备金估计中应用,并且给出了实证分析,针对改进前后的估计效果进行了对比. 本文共分为四个部分. 第一部分为绪论,强调了研究预测未决赔款准备金方法的意义,以及国内外学者对其研究的进展情况.在这样的研究背景下,给出了本文的整体架构,以及本文的创新与不足. 第二部分介绍了未决赔款准备金的确切定义以及分类,阐述了对其评估的必要性.这部分介绍了未决赔款准备金的几种传统确定性评估方法.链梯法是最常用的一种评估方法,但是仅考虑了赔款额这一信息,为了使评估更为准确,案均法引入了赔款次数这一重要的信息.然而这两种确定性方法都忽略了已结案赔款额度与已报案未决赔款准备金的关系,基于此,进一步给出了准备金进展法.这部分给出了一个具体实例,通过实例介绍了这三种方法的基本步骤. 第三部分介绍了一种动态的准备金评估方法——Bootstrap方法,介绍了它的基本步骤.Bootstrap方法的抽样过程中,由于原始样本的观察值确定,抽取随机,很有可能抽取与原始样本相似,或者偏离原始样本较大的再生样本.针对Bootstrap方法中可能存在的问题,本文介绍了一种改进的Bootstrap方法,给出了其基本数学思想,并且相应的给出了改进前后的Bootstrap方法在传统链梯法中的应用的基本步骤. 第四部分基于前人的理论研究基础,给出了具体的实例,运用EXCEL VBA,分别运用Bootstrap方法以及改进后的Bootstrap方法对未决赔款准备金的数据进行了模拟.最后,通过对实际数据的拟合分析在链梯法中应用的效果进行了比较.
[Abstract]:Since the reform and opening up , our country ' s insurance industry has maintained a rapid development progress and has achieved remarkable achievements . But our country ' s insurance market is still in the primary stage of development . It is very important to develop and improve the core competence .

At present , the most widely used methods of reserve extraction are deterministic model estimation methods , such as ChainLadder Method , Case - By - Case Method , B - F method , Reserve progress method , etc . However , this method has been applied to reserve estimation by using modern probability and mathematical statistics .

This paper is divided into four parts .

The first part is the introduction , emphasizes the significance of studying the method of predicting outstanding compensation reserves and the progress of scholars at home and abroad . In the background of this research , this paper gives the whole structure of this paper , and the innovation and deficiency of this paper .

The second part introduces the precise definition and classification of the reserve for the outstanding claims , and expounds the necessity of the assessment . This part introduces several traditional certainty evaluation methods for the reserve of the outstanding compensation .

In the third part , a dynamic reserve assessment method _ bootstrap method is introduced , and its basic procedure is introduced . In the sampling process of the bootstrap method , it is possible to extract the reproduced sample which is similar to the original sample or deviating from the original sample . For the possible problems in the bootstrap method , this paper introduces an improved bootstrap method , gives the basic mathematical thought , and gives the basic steps for the application of the bootstrap method before and after the improvement in the traditional chain ladder method .

In the fourth part , based on the former theory research foundation , the concrete examples are given , the bootstrap method and the improved bootstrap method are used to simulate the data of the reserve of the outstanding claims . Finally , the effect of the application in the chain ladder method is compared by fitting the actual data .

【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F840

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