Academic Report of School of Mathematical Sciences [2026] No. 007

(Series Report for High-Level University Construction No. 1266)

Title：Learning to optimally stop a diffusion process

Speaker：Zuoquan Xu (The Hong Kong Polytechnic University)

Time：10:30-11:30, Jan. 20, 2026

Location：Huixing Building 514

Abstract：We study optimal stopping for diffusion processes with unknown model primitives within the continuous-time reinforcement learning (RL) framework developed by Wang et al. (2020), and present applications to option pricing and portfolio choice. By penalizing the corresponding variational inequality formulation, we transform the stopping problem into a stochastic optimal control problem with two actions. We then randomise controls into Bernoulli distributions and add an entropy regulariser to encourage exploration. We derive a semi-analytical optimal Bernoulli distribution, based on which we devise RL algorithms using the martingale approach established in Jia and Zhou (2022a). We establish a policy improvement theorem and prove the fast convergence of the resulting policy iterations. We demonstrate the effectiveness of the algorithms in pricing finite-horizon American put options, solving Merton's problem with transaction costs, and scaling to high-dimensional optimal stopping problems. In particular, we show that both the offline and online algorithms achieve high accuracy in learning the value functions and characterising the associated free boundaries. This is a joint work with Min Dai, Yu Sun, and Xun Yu Zhou.

Speaker Profile：Professor Zuoquan Xu obtained his bachelor's, master's, and doctoral degrees from Nankai University, Peking University, and The Chinese University of Hong Kong, respectively. He previously served as a Nomura Financial Mathematics Research Fellow at the Institute of Mathematics at the University of Oxford, UK, and concurrently held the position of Corresponding Research Fellow at the Oxford-Man Institute. He is currently a faculty member in the Department of Applied Mathematics at The Hong Kong Polytechnic University, focusing on theoretical research in financial mathematics. His research encompasses quantitative behavioral finance, portfolio theory, and insurance contract theory. He has delivered academic presentations at numerous prestigious global academic institutions and conferences, and has led multiple projects funded by the National Natural Science Foundation of China and the Research Grants Council of Hong Kong. His major academic achievements have been published in prestigious international journals such as Mathematical Finance, Annals of Applied Probability, Finance and Stochastics, Mathematics of Operations Research, SIAM Journal on Financial Mathematics, Quantitative Finance, and Insurance: Mathematics and Economics. He currently serves on the editorial board of the renowned international journal Mathematics of Operations Research.

Faculty and students are welcome to attend!

Invited by: Hailing Dong

School of Mathematical Sciences

January 13, 2026