车险索赔次数预测模型的扩展与应用  

Extended Models for Claim Frequency of Auto Insurance with Practical Applications

作　　者：王选鹤[1] 孟生旺[2,3] 杨默 WANG Xuan-he;MENG Sheng-wang;YANG Mo

机构地区：[1]东北财经大学金融学院 [2]中国人民大学应用统计科学研究中心 [3]中国人民大学统计学院

出　　处：《保险研究》2018年第11期82-92,共11页Insurance Studies

基　　金：国家自然科学基金青年项目(71601037);国家社科基金重大项目(16ZDA052);教育部人文社会科学重点研究基地重大项目(16JJD910001);辽宁省社会科学规划基金青年项目(L15CJY006);东北财经大学青年科研项目(DUFE2017Q03)

摘　　要：我国启动的二期商业车险费率市场化改革,进一步扩大了保险公司车险定价的自主权,对于保险公司的定价能力提出了更高要求。传统上基于广义线性模型的定价方法,不能同时刻画车险索赔次数的过离散、零膨胀和异质性,为此,本文对传统的泊松回归模型进行了扩展:首先对泊松分布进行混合,得到混合泊松分布,主要包括负二项分布和泊松-逆高斯分布,用以刻画索赔次数的过离散特征;然后调整混合泊松分布在零点的概率,构建零膨胀混合泊松分布模型,主要包括零膨胀负二项分布和零膨胀泊松-逆高斯分布,用以同时刻画索赔次数的过离散和零膨胀特征;最后通过对零膨胀混合泊松分布进行有限混合,构建具有分层结构的有限混合零膨胀负二项分布和有限混合零膨胀泊松-逆高斯分布(统称为扩展的混合泊松分布),用以同时刻画索赔次数的过离散、零膨胀和异质性。在扩展的混合泊松分布中,可以在所有的分布参数中引入解释变量(费率因子),从而建立GAMLSS回归模型,并用EM迭代算法估计回归系数。通过实证分析国内一组车险保单的索赔数据发现,该模型结构灵活,具有较强的可扩展性,可以为车险费率厘定提供有益参考和借鉴。Automobile insurance premium rating is currently under the second phase of marketization reform in China.The reform further expands the autonomy of automobile insurance rating and accordingly,has higher requirements on the pricing ability of insurance companies.The traditional generalized linear model pricing methods cannot describe all the distribution characteristics of over-dispersion,zero-inflation,and heterogeneity for auto insurance claim frequency.Based on the Poisson distribution,this paper constructed a mixed Poisson distribution model,including the negative binomial distribution and the Poisson-inverse Gaussian distribution,to describe the over-dispersed feature of the claim frequency.Furthermore,by inflating the probability of zero,a zero-inflated mixed Poisson distribution model was constructed,including zero-inflated negative binomial distribution and zero-inflated Poisson- inverse Gaussian distribution,to simultaneously describe over-dispersion and zero-expansion characteristics of claim frequency.Finite mixed zero-inflated negative binomial distribution and finite mixed zero-inflated Poisson-inverse Gaussian distribution were then constructed,which was referred to as extended mixed Poisson distribution,to describe all the distribution characteristics of over-dispersion,zero-inflation,and heterogeneity for automobile insurance claim frequency.Under the finite mixed zero-inflated negative binomial distribution and the finite mixed zero-inflat- ed Poisson-inverse Gaussian distribution,explanatory variables (rate factors)were introduced into all the distribution parameters to establish the GAMLSS model,and regression coefficients were estimated by the EM iterative algo- rithm.The application of the model to a data set of automobile insurance claims showed that the new model had a flexible structure and strong scalability,which could provide useful reference for auto insurance premium rating.

关 键 词：汽车保险 混合分布 过离散 零膨胀 GAMLSS 

分 类 号：F840.65[经济管理—保险] F224.7