中文摘要：

索赔频率预测是非寿险费率厘定的重要组成部分。最常使用的索赔频率预测模型是泊松回归和负二项回归,以及与它们相对应的零膨胀回归模型。但是,当索赔次数观察值既具有零膨胀特征,又存在组内相依结构时,上述模型都不能很好地拟合实际数据。为此,本文在泊松分布、负二项分布、广义泊松分布、P型负二项分布等条件下分别建立了随机效应零膨胀损失次数回归模型。为了改进模型的预测效果,对于连续型的解释变量,还引入了二次平滑项,并建立了结构性零比例与解释变量之间的回归关系。基于一组实际索赔次数数据的实证分析结果表明,该模型可以显著改进现有模型的拟合效果。

英文摘要：

It＇ s an important work to predict claim frequency in non-life insure ratemaking. Poisson and negative binomial regression models and the corresponding zero-inflated modes are widely used in prediction of claim frequency. However, when claim data includes zero-inflated characteristics and inter dependency structure, these models can not fit the data well. This paper considers to construct random effect zero-inflated claim frequency regression models under the condition of Poisson distribution, negative binomial distribution, generalized Poisson distribution, and P type negative binomial distribution. In order to improve prediction accuracy, we introduce quadratic smooth item in the models and also build a regression between structural zero probability and rating factors. The models are applied to a set of insurance loss data and the result shows that the goodness-of-fit can be effectively improved.