基于偏正态随机效应模型的信度保费

信度模型是非寿险经验费率厘定的主要方法。传统的Buhlmann-Straub信度模型可以表示为随机截距模型，而随机截距模型假设随机效应服从正态分布。在实际的保险损失数据中，部分个体风险的损失可能远远高于总体平均水平，从而使得不同个体风险之间的风险差异呈现右偏特征。在这种情况下，Buhlmann-Straub模型有可能低估高风险的信度保费。本文在随机截距模型中假设随机效应服从偏正态分布，求得了偏正态随机效应假设下的信度保费。可以证明，Buhlmann-Straub信度保费是其特例。模拟分析和实证研究的结果都表明，偏正态随机效应假设下的信度模型可以更好地预测高风险的信度保费，从而改进传统信度模型的保费估计结果。

Credibility Premium Based on Skew-Normal Random Effect Model

Credibility models are main methods of experience ratemaking for non-life insurance. Classical Buhlmann-Straub credibility model can be expressed as a random intercept model. Random intercept model assumes that the random effect is normally distributed. In insurance reality, some individual risks may cause much higher losses than the population average. In this case, random effect is right-skewed and Buhlmann-Straub model may under-estimate the credibility premium with higher risks. The paper assumes that the random effect is skew-normally distributed in random intercept model, and a new credibility premium may be calculated. It can be shown that Buhlmann-Straub model is included in this new model as a special case. Simulation study and case study show that the new credibility model improves the credibility premium of higher risks.