Mathematics Seminar | Bingyan Han
Online Mathematics seminar by Dr Bingyan Han (University of Michigan), held on 1 June 2022.
Title: Distributionally Robust Risk Evaluation with Causality Constraint and Structural Information
Abstract: We consider the distributionally robust evaluation of expected function values over temporal data. A set of alternative measures is characterized by the causal optimal transport. We prove the strong duality and recast the causality constraint as minimization over an infinite-dimensional test function space. We approximate test functions by neural networks and prove the sample complexity with Rademacher complexity. Moreover, when structural information is available to further restrict the ambiguity set, we prove the dual formulation and provide efficient optimization methods. Simulation of stochastic volatility and empirical analysis of stock indices demonstrate that our framework offers an attractive alternative to the classic optimal transport formulation. The preprint is available at https://arxiv.org/abs/2203.10571.
Bio: Bingyan HAN is an incoming Postdoctoral Assistant Professor (non-tenure track) at the Department of Mathematics, University of Michigan. His research focuses on mathematical finance, especially model uncertainty, time-inconsistency, and rough volatility models. His works appear in Finance and Stochastics, Quantitative Finance, SIAM Journal on Financial Mathematics, etc. Previously, he was an Assistant Professor at the BNU-HKBU United International College. He received his Ph.D. degree from The Chinese University of Hong Kong in 2020 and his Bachelor’s degree from the University of Science and Technology of China in 2016.