Columbia-NYU Financial Engineering Colloquium: Min Dai & Yufei Zhang

This event is free, but registration is required.

Min Dai

Chair, Professor of Applied Statistics and Financial Mathematics in the Department of Applied Mathematics and the School of Accounting and Finance at The Hong Kong Polytechnic University (PolyU)

Title

Option Exercise Games and the q Theory of Investment

Abstract

In their study of the Cournot singular control real-option game introduced by Grenadier (2002), Back and Paulsen (2009) advocate using closed-loop equilibria to characterize firm strategies, allowing firms to dynamically respond to their competitors’ actions over time. They identify one such equilibrium in which firms compete intensely, resulting in zero profits, and raise open questions concerning the formal definition of closed-loop equilibria and the existence of alternative equilibria that yield positive profits. A key challenge stems from the overlapping action regions of firms, which precludes characterization through traditional smooth-pasting conditions or variational inequalities. In this talk, we provide a rigorous definition of closed-loop equilibrium and develop a systematic method to explicitly identify infinitely many closed-loop equilibria in closed form. Building on this, we propose a duopolistic q-theory of investment. Our results show that, across all closed-loop equilibria, firms invest at a pace slower than that in the closed-loop equilibrium identified by Back and Paulsen (2009), yet faster than in the open-loop equilibrium originally proposed by Grenadier (2002). Consequently, firm values in the newly identified closed-loop equilibria exceed those in Back and Paulsen’s equilibrium but remain below those in the open-loop equilibrium. This work is joint with Zhaoli Jiang and Neng Wang.

Bio

Min Dai is Chair Professor of Applied Statistics and Financial Mathematics in the Department of Applied Mathematics and the School of Accounting and Finance at The Hong Kong Polytechnic University (PolyU). Prior to joining PolyU in 2021, he taught at the National University of Singapore and Peking University after earning his PhD from Fudan University in 2000. His research focuses on financial derivative pricing, portfolio selection under market imperfections, corporate finance, and financial technology. He has published in peer-reviewed journals across multiple disciplines, including Journal of Economic Theory, Journal of Finance, Management Science, Mathematical Finance, Review of Financial Studies, and SIAM Journals. He currently serves as co-editor of Digital Finance and sits on the editorial boards of several academic journals, including Operations Research, Finance and Stochastics, Journal of Economic Dynamics and Control, and SIAM Journal on Financial Mathematics.

Yufei Zhang

Associate Professor in Mathematical Finance and Machine Learning in the Department of Mathematics at Imperial College London

Title

The alpha-Potential Game Paradigm: Theory, Algorithms, and Applications

Abstract

Designing and analyzing non-cooperative multi-agent systems that interact within shared dynamic environments is a central challenge across many established and emerging applications, including autonomous driving, smart grid management, and e-commerce. A key objective in these systems is to identify Nash equilibria, where no agent can benefit by unilaterally deviating from its strategy. However, computing such equilibria is generally intractable unless specific structural properties of the interactions can be leveraged.

Recently, we have developed a new paradigm known as the alpha-potential game framework for studying dynamic games. This talk illustrates the framework through a class of dynamic games motivated by game-theoretic models of crowd motion. We show that analyzing alpha-Nash equilibria reduces to solving a finite-dimensional control problem. Beyond providing viscosity and verification characterizations for general games, we examine in detail how spatial population distributions and interaction rules shape the structure of alpha-Nash equilibria, in particular for crowd motion games.

Theoretical insights are complemented by numerical experiments based on policy gradient algorithms, which highlight the computational advantages of the alpha-potential game framework for efficiently computing Nash equilibria in dynamic multi-agent environments.

Bio

Yufei Zhang is an Associate Professor in Mathematical Finance and Machine Learning in the Department of Mathematics at Imperial College London, where he also serves as Co-Director of the MSc in Mathematics and Finance program. Before joining Imperial, he was an Assistant Professor in the Department of Statistics at the London School of Economics and Political Science. He obtained his PhD from the Mathematical Institute at the University of Oxford in 2021.

Yufei’s research lies at the intersection of stochastic control, game theory, machine learning theory, and mathematical finance, with a particular focus on developing new theoretical foundations and algorithmic frameworks for complex decision-making in dynamic and uncertain environments.