个体数据模型准备金评估：带有插补值的多元核密度估计方法

发布时间：2018-04-03 04:05

本文选题：未决赔款准备金　切入点：个体数据　出处：《华东师范大学》2013年硕士论文

【摘要】：非寿险责任准备金是财险公司最主要的负债项目,因此非寿险责任准备金评估的充足性和准确性在很大程度上影响着保险公司的偿付能力和盈利能力。当前,财险公司大多采用传统的准备金方法,如链梯法、B-F法来评估计提未决赔款准备金。这些方法忽略了赔款数据本身具有的随机性,得到准备金的点估计的同时并不能给出估计的精度。而且使用聚合数据丢失了个体数据中的许多有效信息,影响了准备金预测的准确性。因此,我们要发展一些基于个体数据的随机性模型来提高准备金预测的准确性。本文主要的研究对象是基于个体数据的已发生已报告未决赔款准备金(Reported But Not Settled,以下简称RBNS)评估,本文的第二章中对于一个非常弱的无分布假设模型下给出了一种利用带有插补值的多元核密度估计方法的RBNS准备金评估方法。该方法的核心思想是将需要估计的流量三角形下三角部分看成单调缺失数据,利用同一事故年的已知数据对这些缺失数据进行插补,插补完成后与已知数据一起对赔款额进行多元核密度估计,当作赔款额的分布估计。最后用赔款额随机变量期望的估计作为RBNS准备金的估计。这种方法的优点在于对于赔款分布没有任何假设,适用范围非常广；得到了赔款分布的估计,可以利用随机变量的不同数字特征来进行准备金的评估；而且能充分利用个体数据的信息。结果表明：带有插补值的多元核密度估计方法所得到的准备金估计要比基于聚合数据下链梯法的估计要好。
[Abstract]:Non-life liability reserve is the most important liability item of property insurance company, so the adequacy and accuracy of evaluation of non-life insurance liability reserve greatly affect the solvency and profitability of insurance company.At present, most property insurance companies use traditional reserve methods, such as chain ladder method B-F method to evaluate the outstanding claims reserve.These methods ignore the randomness of the compensation data itself and can not give the accuracy of the estimation while obtaining the point estimation of the reserve.Moreover, aggregate data is used to lose a lot of valid information in individual data, which affects the accuracy of reserve forecast.Therefore, we should develop some stochastic models based on individual data to improve the accuracy of reserve forecast.The main research object of this paper is the evaluation of But Not set based on individual data.In the second chapter of this paper, for a very weak distribution-free hypothesis model, a RBNS reserve evaluation method using the multivariate kernel density estimation method with interpolation value is presented.The core idea of this method is to treat the lower triangular part of the triangle which needs to be estimated as the monotone missing data, and to use the same method.The missing data are interpolated by the known data of an accident year. After the interpolation is completed, the multi-element kernel density estimation of the compensation amount is carried out together with the known data, which is regarded as the distribution estimation of the compensation amount.Finally, the RBNS reserve is estimated by the expected estimate of the random variable of compensation.The advantage of this method is that there are no assumptions about the distribution of compensation, and the scope of application is very wide, and the estimation of the distribution of compensation is obtained, and the reserve can be evaluated by using different numerical characteristics of random variables.And can make full use of the information of individual data.The results show that the estimate of reserve by the method with interpolation value is better than that by the chain ladder method based on aggregate data.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O212.4;F840.3

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