基于广义多项式混合效应模型非寿险信度费率厘定

Non-life Insurance Credibility Ratemaking Based on Generalized Polynomial Mixed Effect Models

广义线性混合效应模型在非寿险精算中有着广泛的应用。然而,广义线性混合效应模型假设模型的系统成分随时间变化是线性的。但在精算实践中,系统成分随时间的变化并非线性,而是不同时间系统成分的变化率可能不同。当变化为非线性时,通常将时间变量的多项式函数加入广义线性混合效应模型的系统成分中,从而得到广义多项式混合效应模型。文章将广义多项式混合效应模型用于信度费率厘定中,并用美国马塞诸州城镇车身损失责任保险的损失额数据进行实证分析,研究表明,当系统成分随时间非线性变化时,用广义多项式混合效应模型比用广义线性混合效应模型预测效果好。

Generalized linear mixed effect model has been widely used in the non-life insurance life contingencies. However, the generalized linear mixed effects model assumes that the model＇ s system components change linearly with time. But in the actuarial practice, system components change with time is non-linear, and the system components change rate of with time may be different. When the change is non-linear, polynomial function of time variable is usually added to the system component of generalized linear mixed effect model, hence the generalized polynomial mixed effect model. This paper uses the generalized polynomial mixed effect in credibility rating to make an empirical analysis by use of the loss data of town car-body loss liability insurance in Massachusetts. The research shows that when the system components change with time is non-linear, generalized polynomial mixed effect model is better than generalized linear mixed effect model.