Generalized Expected-Shortfalls Based on Distortion Risk Measures

In this talk, we present explicit representations of generalized Expected-Shortfall (ES) based on a distortion risk measure with a general distortion function, not necessarily differentiable, as well as the reverse generalized ES optimization formula. Applying this reverse optimization formula, we obtain the expressions of the worst-case value and the worst-case distribution function of a distortion risk measure of a stop-loss random variable over a distributional uncertainty set induced via the Wasserstein distance of order 2 and the first two moments constraints. Properties of the buffered probability of exceedance (bPOE) based on the generalized ES are also investigated, and it is shown that the corresponding bPOE can be computed by solving a smooth one-dimensional convex optimization problem.

This is a joint work with Zhenfeng Zou, Shuyu Gong and Meng Guan.

报告人简介：胡太忠，中国科学技术大学管理学院教授，1994年于中国科大获概率论与数理统计专业博士学位，2001年晋升为教授，2004年入选教育部“新世纪优秀人才支持计划”，2014年获安徽省教学名师称号。研究领域包括精算理论、随机比较、统计相依、极值理论和可靠性数学等。现为国际期刊Insurance: Mathematics & Economics, Probability in the Engineering and Informational Sciences, Quality Technology & Quantitative Management的副主编，Communications in Mathematics and Statistics的编委，《中国科学技术大学学报》学科主编。