School of Mathematical Sciences Academic Report [2025] No. 024

(High-Level University Construction Series Report No. 1047)

Lecture Title: Robust Λ-quantiles and Extremal Distributions

Speaker: Dr. Han Xia (Assistant Professor, Nankai University)  

Date & Time: 10:00–11:00 AM, April 11, 2025  

Venue: Room 514, Huixing Building (Science and Technology Building), Yuehai Campus, Shenzhen University  

Abstract: In this paper, we investigate the robust models for Λ-quantiles with partial information regarding the loss distribution, where Λ-quantiles extend the classical quantiles by replacing the fixed probability level with a probability/loss function Λ. We find that, under some assumptions, the robust Λ-quantiles equal the Λ-quantiles of the extreme distributions. This finding allows us to obtain the robust Λ-quantiles by applying the results of robust quantiles in the literature. Our results are applied to uncertainty sets characterized by three different constraints respectively: moment constraints, probability distance constraints via Wasserstein metric, and marginal constraints in risk aggregation. We obtain some explicit expressions for robust Λ-quantiles by deriving the extreme probabilities for each uncertainty set. Those results are also applied to optimal portfolio selection and optimal reinsurance under model uncertainty.  

Biography: Dr. Han Xia joined the School of Mathematical Sciences at Nankai University in 2022 and is currently a Lecturer in the Department of Probability and Statistics. She received her Ph.D. in Statistics from Nanjing Normal University in 2020, followed by postdoctoral research in the Department of Actuarial Science and Statistics at the University of Waterloo, Canada (2020–2022). Her research focuses on insurance actuarial science, quantitative risk management, and risk sharing. She has published academic papers in journals such as Insurance: Mathematics and Economics, SIAM Journal on Control and Optimization, Mathematical Finance, and Management Science.  

All faculty and students are welcome to attend!

Invited by: Jingchao Li

School of Mathematical Sciences  

April 10, 2025