报告题目：Higher-order Gini indices: An axiomatic approach

报告时间：2026年11月6日 11：00-12：00

地点：动漫a片 106会议室

报告人：韩霞

摘要：Via an axiomatic approach, we  characterize the family of n-th order Gini deviation, defined as the expected range over n independent draws from a distribution, to quantify joint dispersion across multiple observations. This family extends the classical Gini deviation, which relies solely on pairwise comparisons. The normalized version is called a high-order Gini coefficient.  The generalized indices grow increasingly sensitive to tail inequality as n increases, offering a more nuanced view of distributional extremes.  The higher-order Gini deviations admit a Choquet integral representation, inheriting the desirable properties of coherent deviation measures. Furthermore, we show that both the n-th order Gini deviation and the n-th order Gini coefficient are statistically n-observation elicitable, allowing for direct computation through empirical risk minimization. Data analysis using World Inequality Database data reveals that higher-order Gini coefficients  capture disparities that the classical Gini coefficient may fail to reflect, particularly in cases of extreme income or wealth concentration.

报告人简介：韩霞，南开大学数学科学院教授，研究方向为保险精算、量化风险管理及风险分担。在期刊Management Science、Mathematical Finance、SIAM Journal on Control and Optimization、Insurance: Mathematics and Economics等发表学术论文20余篇，主持国家自然科学基金青年项目、面上项目。