Deep quantile and deep composite triplet regression
针对协变量对条件分布主体和尾部影响不同的问题，提出以条件分位数为拼接点的深度复合回归模型，并引入严格一致的评分函数来估计分位数及上下期望短缺，在意外险数据上表现优于传统方法。
A main difficulty in actuarial claim size modeling is that covariates may have different effects on the body of the conditional distribution and on its tail. To cope with this problem, we introduce a deep composite regression model whose splicing point is given in terms of a quantile of the conditional claim size distribution (rather than a constant). This allows us to simultaneously fit different regression models in the two different parts of the conditional distribution function. To facilitate M-estimation for such models, we introduce and characterize the class of strictly consistent scoring functions for the triplet consisting of a quantile, as well as the lower and upper expected shortfall beyond that quantile. In a second step, this elicitability result is applied to fit deep neural network regression models. We demonstrate the applicability of our approach and its superiority over classical approaches on a real data set from accident insurance.