车险三责险损失金额回归模型的比较和应用.pdf

摘 要 本文基于广义线性模型的基本原理,对车险商业三责险定价中通常遇到的 两种数据组织形式即个体保单数据和分类汇总的保单组合数据的定价模型进行 了讨论。对于个体保单数据,在假设每张个体保单损失变异系数相同的条件下 就纯保费建立了零调整的广义指数、伽玛回归的乘法模型,在放宽个体保单损 失变异系数相同的假设下就纯保费建立了零调整的逆高斯、对数正态回归的乘 法模型。对于分类汇总的保单组合数据,在假设不同风险类别每次损失额的变 异系数相同的条件下采用广义指数、伽玛、逆高斯、对数正态回归对保单组合 的损失强度建立了乘法模型。昀后采用中国某保险公司商业三责险数据和1977 年瑞士机动车第三方责任险数据对上述模型之间的差异进行了探究。 在第一章介绍了问题的研究背景和意义,以及本文的框架结构。 第二章就车险商业三责险个体保单在其损失金额基于零调整的广义指数、 伽玛、逆高斯、对数正态分布下建立了乘法回归模型。 第三章就分类汇总的保单组合在其损失强度基于广义指数、伽玛、逆高斯、 对数正态分布下建立了乘法回归模型。 第四章对本文用来拟合损失强度的四种分布形式:广义指数、伽玛、逆高 斯、对数正态分布的尾部性质进行了讨论,给出了模型检验的统计量及拟合优 度的测度,并采用两组实际数据就第三章和第四章建立的模型进行了实证研究。 第五章总结了前述分析的结果和本文的不足之处。 关键词:损失强度;广义线性模型1Abstract Based on the basic principles of the generalized linear regression, this paper developed and discussed the pricing models for individual policy data and risk group data, the two common organizations of data in insurance practice. For individual policy data, the paper assumed that the loss amount of each policy had the constant coefficient of variation and applied the Zero Adjusted Generalized Exponential and Zero Adjusted Gamma regressions to build the multiplicative models, then the paper removed the restrictions on the constant coefficient of variation for each policy to build multiplicative models for individual policy data based on Zero Adjusted Inverse Gaussian and Zero Adjusted Lognormal regressions. For risk group data, the paper assumed the loss amount of every accident for each risk group had the constant coefficient of variation and followed the Generalized Exponential, Gamma, Inverse Gaussian or Lognormal distribution, then developed the pricing models for the risk group data. At the end of the paper, these models are applied to two sets of practical loss data to compare their differencesChapter 1 introduces the background of this paperChapter 2 develops multiplicative models for individual policy data based on the Zero Adjusted Generalized Exponential distribution, Zero Adjusted Gamma distribution, Zero Adjusted Inverse Gaussian distribu