有限混合分布在车险费率厘定中的应用

Applicationof Finite Mixture Distributions in Vehicle Insurance Ratemaking

"大数据"时代,保险损失数据结构日益复杂,传统分布类型无法准确、全面地反映数据的分布特征,需要更多灵活的模型,而有限混合分布对于刻画与分析真实索赔次数与索赔额分布提供了一个更多的选择。分析几种典型的有限混合分布,结合gamlss分布族构建了基于不同的有限混合分布的费率厘定模型。以一组车险损失数据为例进行实证分析,结果说明相对于传统的分布类型而言,有限混合分布具有较强的可实施性,有助于改善模型的拟合效果。

In the ＂ Big Data＂ era,the structure of insurance loss data becomes increasingly complex,while traditional distributions cannot reflect the distribution characteristics accurately and comprehensively.As a result,more flexible models for actuarial applications are called for.Finite mixture distributions provide a more choice for characterizing and analyzing the distribution of claim numbers and claim amount.After the analysis of several typical finite mixture distributions,different models with gamlss.family are constructed.As empirical analysis,a set of auto insurance loss data is analyzed.The results indicate that compared to the traditional type of distribution,finite mixture distributions are competing,with a straightforward implementation and optimization,which can help to improve the goodness-of-fit.