This paper deals with the use of parametric quantile regression for the calculation of a loaded premium, based on a quantile measure, corresponding to individual insurance risk. Heras et al. have recently introduced a ratemaking process based on a two-stage quantile regression model. In the first stage, a probability to have at least one claim is estimated by a GLM logit, whereas in the second stage several quantile regressions are necessary for the estimate of the severity component. The number of quantile regressions to be performed is equal to the number of risk classes selected for ratemaking. In the actuarial context, when a large number of risk classes are considered (e.g. in Motor Third Party Liability), such approach can imply an over-parameterization and time-consuming. To this aim, in the second stage, we suggest to apply a more parsimonious approach based on Parametric Quantile Regression as introduced by Frumento and Bottai and never used in the actuarial context. This more conservative approach allows you not to lose efficiency in the estimation of premiums compared to the traditional Quantile Regression.

本文涉及使用分位数分位数回归来基于分位数度量来计算与个人保险风险相对应的带载保费。Heras等。最近引入了基于两阶段分位数回归模型的费率制定过程。在第一阶段，通过GLM logit估计拥有至少一项索赔的概率，而在第二阶段，对于严重程度分量的估计，需要进行几分位数回归。要执行的分位数回归的数量等于为评估而选择的风险类别的数量。在精算环境中，当考虑到大量风险类别时（例如，在“汽车第三方责任”中），这种方法可能意味着过度参数化和耗时。为此，在第二阶段，我们建议根据Frumento和Bottai提出的，基于参数分位数回归的更简化方法，不要在精算环境中使用。与传统的分位数回归相比，这种更为保守的方法使您不会损失保费估算的效率。