统计研究

汽车保险广受社会关注,且在财产保险公司具有举足轻重的地位,因此汽车保险的索赔频率预测模型一直是非寿险精算理论和应用研究的重点之一。目前最为流行的索赔频率预测模型是广义线性模型,其中包括泊松回归、负二项回归和泊松—逆高斯回归等。本文基于一组实际的车险损失数据,对索赔频率的各种广义线性模型与神经网络模型和回归树模型进行了比较,得出了一些新的结论,即神经网络模型的拟合效果优于广义线性模型,在广义线性模型中,泊松回归的拟合效果优于负二项回归和泊松—逆高斯回归。线性回归模型的拟合效果最差,回归树模型的拟合效果略好于线性回归模型。

Auto insurance is widely concerned by the public and plays a very important role in property insurance companies,so claim frequency models of auto insurance have been a focus of theoretical and practical research in non-life actuarial science.Currently generalized linear models(GLM) are very popular in claim frequency modeling,such as Poisson regression,negative binomial regression and Poisson-inverse Gaussian regression.Using a real dataset of auto insurance,the paper compares various GLMs with neural networks and regression tree.The result shows that neural networks are superior to GLMs in fitting the data and Poisson regression is better than negative binomial regression and Poisson-inverse Gaussian regression.Linear regression is the worst one in the models considered in the paper and regression tree is a little better than linear regression model.