Tail Gini functional is a measure of tail risk variability for systemic risks, and has many applications in banking, finance and insurance. Meanwhile, there is growing attention on aymptotic independent pairs in quantitative risk management. This paper addresses the estimation of the tail Gini functional under asymptotic independence. We first estimate the tail Gini functional at an intermediate level and then extrapolate it to the extreme tails. The asymptotic normalities of both the intermediate and extreme estimators are established. The simulation study shows that our estimator performs comparatively well in view of both bias and variance. The application to measure the tail variability of weekly loss of individual stocks given the occurence of extreme events in the market index in Hong Kong Stock Exchange provides meaningful results, and leads to new insights in risk management.

翻译：尾部基尼泛函是衡量系统性风险中尾部风险变异性的指标，在银行、金融和保险领域具有广泛应用。与此同时，定量风险管理中对渐近独立对的研究日益受到关注。本文研究了在尾部渐近独立条件下尾部基尼泛函的估计问题。我们首先在中间水平上估计尾部基尼泛函，然后将其外推至极端尾部。中间水平估计量和极端水平估计量的渐近正态性均得以建立。模拟研究表明，从偏差和方差角度来看，我们的估计量表现良好。将所提方法应用于衡量香港交易所市场指数极端事件发生时个股周度损失的尾部变异性，不仅提供了有意义的结果，还为风险管理带来了新见解。