The 2026 Karl Menger Lecture and Activities

April 13-14, 2026

Menger Lecturer:

Liu Family Professor of Financial Engineering; Director of the Nie Center for Intelligent Asset Management, Columbia University

Menger Lecture Title:

Model-Based and Model-Free: A Tale of Two Paradigms Told from Reinforcement Learning and Generative AI

Menger Lecture Abstract:

In this lecture I will discuss the key connections and differences between the model-based and model-free paradigms from the perspectives of reinforcement learning and generative AI. I will argue that establishing a sufficiently accurate model is both impossible and unnecessary for the ultimate purpose of making optimal decisions, but there is some quantity, one that is an aggregate measure of the model parameters and control actions, that needs to be learned and can indeed be learned efficiently in a data-driven way.

Bio:

Xunyu Zhou is the Liu Family Professor of Industrial Engineering and Operations Research at Columbia University in New York. He was the Nomura Professor of Mathematical Finance, the director of Nomura Center for Mathematical Finance, and the director of Oxford-Nie Financial Big Data Lab at University of Oxford during 2007-2016 before joining Columbia. He previously was the Choh-Ming Li Professor of Financial Engineering and the founding director of the Center for Financial Engineering at Chinese University of Hong Kong.

Zhou is well known for his work in indefinite stochastic LQ control theory and application to dynamic mean—variance portfolio selection, in asset allocation and pricing under cumulative prospect theory, and in general time inconsistent problems. His current research focuses on reinforcement learning in continuous time with possibly continuous state and action spaces and applications to generative AI and intelligent wealth management solutions. At Columbia, he directs the Nie Center for Intelligent Asset Management, a research center funded by a FinTech company. He has addressed the 2010 International Congress of Mathematicians and has been awarded the Wolfson Research Award from The Royal Society (UK), the Outstanding Paper Prize from the Society for Industrial and Applied Mathematics, the Humboldt Distinguished Lecturer, the Alexander von Humboldt Research Fellowship, the Archimedes Lecturer at Columbia, and Distinguished Faculty Teaching Award at Columbia University. He is both an IEEE Fellow and a SIAM Fellow.

Professor Zhou received his Ph.D. in Operations Research and Control Theory from Fudan University in Shanghai in 1989.

Research Seminar, Tuesday April 14, 2025, 10 a.m., Perlstein Hall 131

Title: Data-Driven Merton’s Strategies via Policy Randomization

Abstract: We study Merton’s expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. The agent under consideration is a price taker who has access only to the stock and factor value processes and the instantaneous volatility. We propose an auxiliary problem in which the agent can invoke policy randomization according to a specific class of Gaussian distributions, and prove that the mean of its optimal Gaussian policy solves the original Merton problem. With randomized policies, we are in the realm of continuous-time reinforcement learning (RL) recently developed in Wang et al. (2020) and Jia and Zhou (2022a,b, 2023), enabling us to solve the auxiliary problem in a data-driven way without having to estimate the model primitives. Specifically, we establish a policy improvement theorem based on which we design both online and offline actor–critic RL algorithms for learning Merton’s strategies. A key insight from this study is that RL in general and policy randomization in particular are useful beyond the purpose for exploration – they can be employed as a technical tool to solve a problem that cannot be otherwise solved by mere deterministic policies. At last, we carry out both simulation and empirical studies in a stochastic volatility environment to demonstrate the decisive outperformance of the devised RL algorithms in comparison to the conventional model-based, plug-in method. Joint wok with Min Dai, Yuchao Dong and Yanwei Jia.

Made possible with the generous support of the Menger family, Department of Applied Mathematics, Illinois Institute of Technology, and the Menger Fund.

Guests are encouraged to RSVP

The 2026 Menger Distinguished Lecture will be available for live streaming

2026 Program/Schedule for M&C

Monday, April 13, 2026 (Menger Day)

12:45–1:45 pm SIAM Undergraduate Hour with Professor Xunyu Zhou
Robert A. Pritzker Science Center, Room 116

3:15–4:15 pm Applied Mathematics Faculty Research Overviews
The McCormick Tribune Campus Center (MTCC), Room 723 (Auditorium)

4:30–5:45 pm Poster Exhibit
The McCormick Tribune Campus Center (MTCC), Room 724 (Ballroom)

6–7:15 pm 16th Annual Menger Lecture by Professor Xunyu Zhou:
“Model-Based and Model-Free: A Tale of Two Paradigms Told from Reinforcement Learning and Generative AI”The McCormick Tribune Campus Center (MTCC), Room 723 (Auditorium)

7:15–7:30 pm Menger Student Awards Announcement and Presentation
The McCormick Tribune Campus Center (MTCC), Room 723 (Auditorium)

7:30–9 pm Reception and Alumni Networking
The McCormick Tribune Campus Center (MTCC), Pritzker Club