广义线性模型框架下基于个体数据的RBNS预测

发布时间：2018-07-01 08:18

本文选题：未决赔款 + RBNS准备金　；参考：《华东师范大学》2013年硕士论文

【摘要】：本文基于包含索赔信息、进展信息、结案信息等的个体数据研究非寿险业务的RBNS准备金的预测问题。以往的未决赔款准备金预测在方法上分为确定性方法、随机性方法和比较新的动态性方法,按照这些预测方法所使用的数据可以分为聚合数据模型和个体数据模型,大多方法使用的数据基础是聚合数据,本文则是基于个体数据在广义线性模型的基本假设下对未决赔款准备金进行有效预测。此外本文比较具有创新性的研究了加入个体结案信息这一重要因素后的RBNS准备金预测问题,利用贝叶斯方法结合极大似然估计给出了未决赔款在个体数据下的条件分布,而传统的链梯法及其衍生出的确定性方法得出的是准备金的低阶估计,有的时候并不能满足评估人员的分析需求。由于加入了个体的结案信息,对于同一事故年或者报告年的已观测个案,其进展年份是不同的,因而以往的确定性方法和随机性方法无法合理有效的进行预测。对于已结案个体从原则上是无需考虑的,但是任何信息的丢失都有可能使得评估结果无法达到预期,本文将已结案个体数据作为参数估计的基础,在多元正态分布假设下结合结案时间分布及后验均值给出了多元正态分布情形下RBNS准备金的预测模型,并与传统链梯法模型进行比较。本文的预测模型在稳定性及谨慎性等原则上更为合理有效,综合比较可得出本文预测模型更能满足评估人员的分析需求。
[Abstract]:Based on individual data including claim information, progress information and closure information, this paper studies the prediction of RBNS reserve for non-life insurance business. According to the data used in these forecasting methods, they can be divided into aggregate data model and individual data model, which can be divided into deterministic method, randomness method and relatively new dynamic method. Most of the methods are based on aggregate data, and this paper is based on individual data to effectively predict the pending claims reserve under the basic assumptions of the generalized linear model. In addition, this paper studies the problem of RBNS reserve forecasting after adding the important factor of individual closure information, and gives the conditional distribution of pending claims under individual data by using Bayesian method combined with maximum likelihood estimation. However, the traditional chain ladder method and its derived deterministic method can not meet the needs of the evaluators. Because of adding the case information of the individual, the progress years of the observed cases in the same accident year or reporting year are different, so the previous deterministic methods and stochastic methods can not be reasonably and effectively predicted. In principle, there is no need to consider the individual who has completed the case, but any loss of information may make the evaluation result impossible to achieve the expected results. In this paper, the individual data of the case has been used as the basis of parameter estimation. Under the assumption of multivariate normal distribution, the prediction model of RBNS reserve under the condition of multivariate normal distribution combined with the closed time distribution and the posteriori mean is given, and compared with the traditional chain ladder method. The prediction model in this paper is more reasonable and effective in the principles of stability and caution, and it can be concluded that the prediction model in this paper can meet the needs of the evaluators.
【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】：F224;F840.4

【参考文献】