勷勤数学•专家报告

题      目：Convolution Bounds on Quantile Aggregation

报  告  人：刘杨 副教授  (邀请人：杨舟)

                                         香港中文大学（深圳）

时      间： 9月26日  10：30-11:30

地     点：数科院西楼二楼会议室

报告人简介:

        Yang Liu is an Assistant Professor of Financial Mathematics at The Chinese University of Hong Kong, Shenzhen (CUHKSZ). Before this role, he was a postdoctoral researcher at Stanford University and the University of Waterloo. Dr. Liu earned his Ph.D. and Bachelor’s degree in Mathematics from Tsinghua University. His research spans financial mathematics, actuarial science, operations research, and applied probability, with a focus on quantitative risk management and non-concave utility theory in portfolio optimization. His work has been published in leading journals, including Operations Research, Mathematical Finance, Finance and Stochastics, SIAM Journal on Control and Optimization, and Insurance: Mathematics and Economics. In 2024, Dr. Liu was awarded the First Place in the Best Paper Prize for Young Scholars at the Annual Conference of the Operations Research Society of China (Financial Engineering and Risk Management Branch).

摘      要：

        Quantile aggregation with dependence uncertainty has a long history in probability theory, with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based risk measures, we establish new analytical bounds for quantile aggregation, which we call convolution bounds. Convolution bounds both unify every analytical result available in quantile aggregation and enlighten our understanding of these methods. These bounds are the best available in general. Moreover, convolution bounds are easy to compute, and we show that they are sharp in many relevant cases. They also allow for interpretability on the extremal dependence structure. The results directly lead to bounds on the distribution of the sum of random variables with arbitrary dependence. We discuss relevant applications in risk management and economics. This joint work is with Jose Blanchet, Henry Lam and Ruodu Wang.

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