混合效应模型及其在非寿险费率厘定中的应用

发布时间：2018-12-23 11:43

【摘要】：在非寿险分类费率厘定中,广义线性模型的应用十分普遍,但当某些费率因子的水平数很多时(本文称之为多水平因子),广义线性模型的估计结果将不可靠。解决此类问题的一种方法是把多水平费率因子作为随机效应处理。将多水平费率因子作为随机效应处理可以采取下述三种方法:(1)分别用广义线性模型和信度模型估计普通费率因子和多水平因子,通过广义线性模型与Buhlmann-Straub信度模型的迭代应用预测索赔频率和索赔强度;(2)应用广义线性混合模型分别预测索赔频率和索赔强度;(3)直接对经验纯保费数据建立Tweedie混合效应模型。本文把上述模型应用于中国车损险实际数据的研究结果表明,这三种方法比较接近,但从总体上看,广义线性混合模型的估计结果更加可取。
[Abstract]:In the determination of non-life insurance classification rates, the generalized linear model is widely used, but when the level number of some rate factors is large (called multi-level factors in this paper), the estimation results of generalized linear model will not be reliable. One way to solve this problem is to treat the multi-level rate factor as a random effect. The following three methods can be used to deal with multilevel rate factor as random effect: (1) the general rate factor and multi-level factor are estimated by generalized linear model and reliability model, respectively. The iterative application of generalized linear model and Buhlmann-Straub reliability model is used to predict claim frequency and claim strength. (2) the generalized linear mixed model is used to predict the claim frequency and the claim strength, and (3) the Tweedie mixed effect model is established directly for empirical pure premium data. This paper applies the above model to the actual data of car loss risk in China. The results show that these three methods are close to each other, but in general, the estimation results of generalized linear mixed model are preferable.
【作者单位】：中国人民大学应用统计科学研究中心;
【基金】：教育部重点研究基地重大项目(12JJD790025) 国家自然科学基金项目(71171193)
【分类号】：O212;F840.4

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