GAMLSS模型及其在车损险费率厘定中的应用

GAMLSS and Its Application in Ratemaking of Auto Damage Insurance

在车损险费率厘定中,通常假设索赔频率、索赔强度或纯保费服从指数分布族,并对其均值建立广义线性模型,而假设其他参数对所有风险类别都是固定的常数。这种假设在某些情况下并非成立。GAMLSS模型可以在各种分布假设下同时对一个分布的位置参数、尺度参数和形状参数建立参数或非参数的回归模型,具有很大的灵活性。本文在零调整逆高斯分布假设下把GAMLSS模型应用于我国实际的车损险数据,建立了车损险的费率厘定模型,结果表明,这种模型对车损险实际数据的拟合要优于常用的Tweedie分布假设下的广义线性模型。此外,这种模型厘定的风险保费更加公平合理。

In auto damage insurance ratemaking, it is usually assumed that claim frequency, claim severity or pure premium follow exponential dispersion family, and only the mean is related to explanatory variables in the model and other parameters of the distribution are assumed to be constant for all risk classes. These assumptions are not true in some circumstances. GAMLSS is much more flexible and may relate all parameters （location, scale and shape） of the distribution to explanatory variables through parametric or non-parametric regression models. The paper assumes the pure premium follows zero adjusted inverse Gaussian distribution and applies GAMLSS to auto damage insurance data of China. The result shows that this model can fit the data better tha~ usually used geaeralized linear model under Tweedie distribution assumption and it also can caculate risk premium more resonably and fairly.