学术讲座

报告题目：Distorted optimal transport

报告时间：2024年7月26日16:00

报告地点：湘江楼A927

报告专家：Haiyan Liu

报告摘要：

Classic optimal transport theory is formulated through minimizing the expected transport

cost between two given distributions. We propose the framework of distorted optimal transport

by minimizing a distorted expected cost, which is the cost under a non-linear expectation. This

new formulation is motivated by concrete problems in decision theory, robust optimization,

and risk management, and it has many distinct features compared to the classic theory. We

choose simple cost functions and study different distortion functions and their implications on

the optimal transport plan. We show that on the real line, the comonotonic coupling is optimal

for the distorted optimal transport problem when the distortion function is convex and the

cost function is submodular and monotone. Some forms of duality and uniqueness results are

provided. For inverse-S-shaped distortion functions and linear cost, we obtain the unique form

of optimal coupling for all marginal distributions, which turns out to have an interesting “first

comonotonic, then counter-monotonic” dependence structure; for S-shaped distortion functions

a similar structure is obtained. Our results highlight several challenges and features in distorted

optimal transport, offering a new mathematical bridge between the fields of probability, decision

theory, and risk management. This talk is based on joint work with Bin Wang, Ruodu Wang, and Shengchao Zhuang.

专家简介：

Haiyan Liu is an associate professor in the Department of Mathematics and the Department of Statistics and Probability. She received her Ph.D. in Actuarial Science from the University of Waterloo in 2017. Her research interests include risk measurement and management, reinsurance, applied probability, and model uncertainty.