Asymptotic Analysis in Robust Optimization

Asymptotic Analysis in Robust Optimization
Topic
Asymptotic Analysis in Robust Optimization
Date & Time
Thursday, April 16, 2026 - 17:00 - 18:00
Speaker
Kyunghyun Park, Nanyang Technological University
Location
W923, West Hall, NYU Shanghai New Bund Campus

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Abstract:

In this talk, we first study the sensitivity of robust optimization problems under parametrical uncertainty in an Itô semimartingale setting. An investor seeks to maximize her worst-case cumulative gain, where the worst-case refers to taking into account all possible drift and volatility processes that fall within a ε-neighbourhood of predefined baseline processes. We quantify how sensitive the robust optimization problem is to uncertainty, which can be attained by showing that the robust problem can be approximated as ε ↓ 0 by its baseline counterpart.
 

In the second part, we analyze the scaling limit of multi-period distributionally robust optimization via a semigroup approach. Each period involves a worst-case maximization over distributions in a Wasserstein ball around a reference process. When the Wasserstein ball's radius scales linearly with time, we show that the scaling limit of the multi-period distributionally robust optimization yields a monotone semigroup on Cb, whose generator equals that of the baseline problem plus a perturbation induced by Wasserstein uncertainty. This establishes a connection between robust optimization problems in continuous time and in discrete time.

Biography:

Kyunghyun Park is a Presidential Postdoctoral fellow at Division of Mathematical Sciences of Nanyang Technological University under Prof. Ariel Neufeld since Dec 2022. Prior joining NTU, he served as a Postdoctoral Fellow at Department of Statistics of The Chinese University of Hong Kong under Prof. Hoi Ying Wong. He obtained PhD in Mathematics at Seoul National University under Prof. Myungjoo Kang in Feb 2021. His primary research pursuits lie within applied probability and stochastic optimization, with a specific emphasis on robust optimization, mean-field game / control, and reinforcement learning.

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai

This event is open to the NYU Shanghai community and Math community.