基于参数化分位回归模型的非寿险准备金评估

准备金及其风险边际对保险公司的偿付能力具有决定性影响.均值回归模型在非寿险准备金评估中的应用较为普遍,但需要通过Bootstrap等方法计算准备金的风险边际.分位回归模型可以一次性求得准备金及其风险边际的预测值,所以在非寿险准备金评估中具有独特的应用价值.基于GB2(Generalized Beta type 2)分布建立了一种参数化分位回归模型,该模型首先对GB2分布中的位置参数和尺度参数同时引入流量三角形数据中的事故年和进展年作为解释变量,增加了模型的灵活性;其次,根据模型参数的极大似然估计结果,借助分位数函数的表达式,计算了不同分位数水平下的准备金预测值;最后,利用极大似然估计的渐近性质,通过Delta方法给出了准备金预测值的误差.基于一组增量赔款数据的实证研究结果表明,GB2参数化分位回归模型在非寿险准备金评估及其风险边际的预测中具有良好的应用价值.

Non-life claims reserving based on parametric quantile regression

Non-life reserve and its risk margin determines the solvency of an insurance company. Mean regression models are widely used in non-life claim reserving, but in which risk margins need to be calculated separately by applying Bootstrap and other methods. The risk margin of claims reserve can be obtained directly by quantile regression models, so quantile regression models have unique application value in the non-life claim reserving. Based on the Generalized Beta type 2 (GB2) distribution, a parameterized quantile regression model is established and applied to non-life claim reserving. To increase the flexibility of the model, the accident years and the development years are simultaneously introduced as explanatory variables to the location parameter and the scale parameter in the Generalized Beta type 2 (GB2) distribution. According to the maximum likelihood estimations of the model parameters, with the help of the expression of the quantile function, the predictions of claims reserve at different quantile levels are calculated. By using the asymptotic property of the maximum likelihood estimation, the delta method is used to calculate the error of the claims reserve. An analysis based on a set of incremental claims data shows that the GB2 parametric quantile regression model may be well applied to predict the claims reserve and its risk margin.