多元有序 Logistic 模型在车险索赔次数预测中的应用

新一轮商业车险综合改革对车险的精准定价提出了更高的要求,预测索赔次数是定价中非常重要的一环。泊松分布等计数分布所对应的零膨胀回归模型是常用的预测模型,现有研究主要集中于在此基础上发展出的零膨胀混合泊松模型。但是,混合泊松模型存在混合个数的确定太过主观和模型参数难以直观解释的缺点。为此,本文避免了对计数分布的讨论,将索赔次数作为分类变量,建立了多元有序Logistic回归模型。使用一组2017年的车险索赔数据进行实证分析,表明该模型的预测结果优于现有的零膨胀模型,并且有效提升了尾部概率估计的准确性。本文所讨论的多元有序Logistic回归模型为车险索赔次数预测提供了新思路,并且该模型拥有较强的解释性和灵活性。

The comprehensive reform of commercial auto insurance puts forward higher requirements for accurate pricing of auto insurance,and predicting the claim frequency is a very important part of the pricing.The zero-inflated regression model corresponding to Poisson distribution is a common prediction model.Based on this model,the existing research focuses on the mixed Poisson model.However,the disadvantages of mixed Poisson model are that the determination of mixed number is too subjective and the model parameters are difficult to explain intuitively.Therefore,this paper avoids the discussion of the count distributions,and takes the number of claims as the classification variable,and establishes the ordered logistic regression model.Using a set of auto insurance claim data in 2017,the empirical analysis shows the prediction result is better than the zero-inflation model,and effectively improves the accuracy of tail probability estimation.The ordered logistic regression model discussed in this paper provides a new idea for forecasting claim frequency for auto insurance,and the model has strong interpretability and flexibility.