Based on recent developments in joint regression models for quantile and expected shortfall, this paper seeks to develop models to analyse the risk in the right tail of the distribution of non-negative dependent random variables. We propose an algorithm to estimate conditional tail expectation regressions, introducing generalized risk regression models with link functions that are similar to those in generalized linear models. To preserve the natural ordering of risk measures conditional on a set of covariates, we add extra non-negative terms to the quantile regression. A case using telematics data in motor insurance illustrates the practical implementation of predictive risk models and their potential usefulness in actuarial analysis.

基于分位数和预期不足的联合回归模型的最新发展，本文力求开发模型以分析非负因变量随机分布的右尾风险。我们提出一种估计条件尾部期望回归的算法，引入链接函数与广义线性模型相似的广义风险回归模型。为了保留以一组协变量为条件的风险度量的自然排序，我们在分位数回归中添加了额外的非负项。在汽车保险中使用远程信息处理数据的案例说明了预测风险模型的实际实现及其在精算分析中的潜在用途。