时 间：2024年7月23日14:00 - 15:30
地 点：普陀校区理科大楼A1514
报告人：Haiyan Liu 美国密歇根州立大学副教授
主持人：李丹萍华东师范大学教授
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.
报告人简介：
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.