基于分层广义线性模型的非寿险费率厘定精算模型研究

非寿险业务中的损失数据结构日益复杂,呈现异质性与相关性并存的异象。分层广义线性模型能够突破传统费率厘定精算方法仅分析风险个体同一保单年损失数据的局限,可以提高复杂结构损失数据预测的准确性。基于分层广义线性模型等方法,研究具有多年损失数据的非寿险费率厘定问题,并以车险和工伤补偿保险的两组损失数据为例进行实证分析。研究结果表明,相对于GLM而言,考虑随机效应后GLMM的拟合优度大幅改善,GLMM与HGLM可以更有效地反映不同风险个体的差异,并有利于揭示风险个体在多个保险期内损失的异质性与相关性。

Research on Actuarial Models of Non-life Insurance Ratemaking with Hierarchical Generalized Linear Models

The structure of loss data is becoming more complex in non-life insurance, showing the coexistence of heterogeneity across subjects and correlation between observations.Hierarchical generalized linear models can break through the traditional limitations of ratemaking methods which can only analyze loss data in one policy year, and can improve the accuracy of the prediction of loss data with complex structural.Based on hierarchical generalized linear models, this paper focuses on non-life insurance ratemaking with multi-year loss data.Loss data of auto insurance and workers' compensation insurance are used to carry out empirical analysis.The results show that comparing with GLM, the goodness-of-fit of GLMMs is significantly improved.In addition, GLMMs and HGLMs can effectively reflect the differences between risk individuals, which are helpful to reveal the heterogeneity between different risk individuals and correlation of loss data for the same risk individual over multiple periods.