非寿险定价与索赔准备金评估的分层模型研究

项目名称： 非寿险定价与索赔准备金评估的分层模型研究

项目编号： No.71271121

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 管理科学

项目作者： 张连增

作者单位： 南开大学

项目金额： 54万元

中文摘要： 非寿险定价与索赔准备金评估是非寿险精算学的两大核心专题。标准的广义线性模型已在这两个专题研究得到了充分的应用。本项目针对非寿险数据的特点，即数据结构普遍存在层次性和相关性、数据观测变量分布来自更广泛的分布族，在分层模型的框架下，结合上述两个专题，开展分层模型的理论研究及其在非寿险精算的应用研究，并使用统计软件（R和WinBUGS）进行非寿险分层数据分析、非寿险定价、索赔准备金预测分布随机模拟等定量研究。其中分层广义线性模型的理论及其在非寿险定价与索赔准备金评估的应用是研究重点。同时研究一般的分层广义线性模型和分层信度模型的内在联系。研究内容分五部分：（一）关于广义线性模型、广义可加模型及新扩展；（二）线性混合效应模型和分层线性模型；（三）广义线性混合模型和分层广义线性模型；（四）非线性分层模型和更一般的分层模型；（五）关于位置、尺度和形状的广义可加模型。每一部分研究都结合上述两个专题展开。

中文关键词： 非寿险定价；索赔准备金评估；分层广义线性模型；贝叶斯方法；分层线性模型

英文摘要： Non-life insurance pricing and claims reserving are two key topics in non-life insurance actuarial science. Standard generalized linear models have been fully applied with respect to these two topics. In this project, in response to the characteristics of non-life insurance data, i.e., the data in general has some hierarchical structures and some dependence, and the distributions of the observation variables are among a wide class of the distribution family, we propose to conduct the research on non-life insurance pricing and claims reserving based on the framework of hierarchical models, investigating their applications in those two topics. In addition, we expect to implement some quantitative studies such as non-life insurance hierarchical data analysis, non-life insurance pricing, the simulation of predictive distribution of claims reserves with statistical software R and WinBUGS. Among them the focus is on the theory of the hierarchical generalized linear models theory as well as their applications in non-life insurance pricing and claims reserving. Also the connections between the hierarchical generalized linear models and the hierarchical credibility models are to be explored. The research can be divided into five parts: (1) research about generalized linear models, generalized additive models, and their

英文关键词： Non-Life Insurance Pricing；Claims Reserving；Hierarchical Generalized Linear Models；Bayesian Methods；Hierarchical Linear Models