非寿险定价与索赔准备金评估的分层模型研究

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 recent generalizations. (2) research about linear mixed effects models and hierarchical linear models. (3) research about generalized linear mixed models and hierarchical generalized linear models. (4) research about non-linear hierarchical models and more general hierarchical models. (5) research about generalized additive models for location, scale and shape. Each part of the research consists of both theoretical aspects and applications as regards non-life insurance pricing and claims reserving.

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。

本项目针对非寿险数据的特点（即数据响应变量分布来自更广泛的分布族、数据结构普遍存在层次性和相关性），结合非寿险精算学中的两大核心问题（即非寿险定价与索赔准备金评估），系统地开展了分层模型（或混合模型）的理论研究及其应用研究，其中分层广义线性模型的理论及其应用研究是重点。在项目研究中，使用统计软件（R和WinBUGS）进行定量分析研究。研究内容可分为四个方面：（1）广义线性模型、广义可加模型及其扩展。（2）线性混合模型（LMM）和分层线性模型（HLM）。（3）广义线性混合模型（GLMM）和分层广义线性模型（HGLM）。（4）考虑位置、尺度和形状的广义可加模型（GAMLSS）。对前三个方面，本项目研究非常深入系统，并取得了丰富的研究成果，对第四个方面的研究有待进一步深入。项目研究成果包括已标注论文36篇，其中代表性的成果发表于统计研究和SCI期刊；培养博士生4名，硕士生8名；项目研究成果转化为精算研究生教学内容；积累了本领域的丰富的研究文献，为后续研究打下了扎实的基础。在开展项目研究的过去五年，发现与本项目相关的最新研究文献一直在不断出现。本项目选题在国际统计与精算领域发展非常迅速，是研究前沿热点，在该方向上继续开展研究很有价值。