Renyuan Xu

Renyuan Xu

About & Research

I am an assistant professor in the Department of Management Science and Engineering at Stanford University. I am also affiliated with the Institute of Computational and Mathematical Engineering (ICME) and the Stanford Theory Group.

Prior to joining Stanford, I held positions at New York University and the University of Southern California (2021–2025) and was a Hooke Research Fellow at the Mathematical Institute, University of Oxford (2019–2021). I received my Ph.D. in 2019 from the Department of Industrial Engineering and Operations Research at the University of California, Berkeley, where I was very fortunate to be advised by Xin Guo.

My research interests include mathematical finance, stochastic analysis, stochastic control and games, and machine learning theory. I am also interested in interdisciplinary work connecting applied probability, statistics, and optimization, with applications to high-stakes decision-making problems in large-scale systems, including finance and economics. Recent topics include:

  • Mathematical foundations of generative AI
  • Optimal stopping and dynamic information acquisition
  • Stochastic control, stochastic games, and mean-field games
  • Reinforcement learning theory
  • Applications in market microstructure and risk management

Recent & upcoming activities

Working papers & preprints

Diffusion Models for Dynamic Volatility Surface Generation and Data-driven Hedging

with Yinbin Han, Jack Yuxiang Zhang, Manuel Torres and Fernando Acero (2026)

Submitted arXiv

Weak-to-Strong Learning in Decision Making

with Jingwei Ji (2026)

Submitted arXiv

Expressivity and Statistical Trade-offs in Diffusion Policy Learning

with Viet Vu, Jiacheng Zhang and Yufei Zhang (2026)

Submitted arXiv

Diffusion Models for Adaptive Sequential Data Generation

with Haoyang Cao, Minshuo Chen and Yinbin Han (2026)

Submitted arXiv Code

One-Step Generative Modeling via Wasserstein Gradient Flows

with Jiaqi Han, Puheng Li, Qiushan Guo, Stefano Ermon and Emmanuel J. Candès (2026)

Submitted arXiv Project

Scalable Bi-causal Optimal Transport via KL Relaxation and Policy Gradients

with Haoyang Cao, Jesse Hoekstra, Yumin Xu and Ruixun Zhang (2026)

Submitted arXiv

Reinforcement Learning in Real Option Models

with Jodi Dianetti and Giorgio Ferrari (2026)

Submitted arXiv

Schrödinger Bridge with Transport Relaxation

with Yifan Jiang and Luhao Zhang (2026)

Submitted arXiv

Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach

with Zhengyi Guo and Wenpin Tang (2026)

Submitted arXiv Code

Schrödinger Bridge for Generative AI: Soft-constrained Formulation and Convergence Analysis

with Jin Ma and Ying Tan (2025)

Revision, Mathematical Finance arXiv

Adaptive Partitioning and Learning for Stochastic Control of Diffusion Processes

with Hanqing Jin and Yanzhao Yang (2025)

Submitted arXiv

Entropy Regularization in Mean-Field Games of Optimal Stopping

with Jodi Dianetti, Roxana Dumitrescu and Giorgio Ferrari (2025)

Revision, SIAM Journal on Control and Optimization arXiv

Multi-Task Dynamic Pricing in Credit Market with Contextual Information

with Jingwei Ji and Adel Javanmard (2024)

Submitted SSRN

Exploratory Optimal Stopping: A Singular Control Formulation

with Jodi Dianetti and Giorgio Ferrari (2024)

Submitted arXiv

Periodic Trading Activities in Financial Markets: Mean-field Liquidation Game with Major-Minor Players

with Yufan Chen, Lan Wu and Ruixun Zhang (2024)

Submitted SSRN

Decision Making Under Costly Sequential Information Acquisition: The Paradigm of Reversible and Irreversible Decisions

with Thaleia Zariphopoulou and Luhao Zhang (2023)

Revision, Mathematics of Operations Research SSRN

Implicit Regularization and Convergence of Gradient Descent for Deep Residual Networks

with Rama Cont and Alain Rossier (2022)

Submitted arXiv

Asymptotic Analysis of Deep Residual Networks

with Rama Cont and Alain Rossier (2022)

Submitted arXiv

Risk-sensitive Markov Decision Process and Learning under General Utilities

with Zhengqi Wu (2023)

Revision, JMLR SSRN

Linear-quadratic Gaussian Games with Asymmetric Information: Belief Corrections Using the Opponents Actions

with Huining Yang and Ben Hambly (2023)

Revision, SIAM Journal on Control and Optimization arXiv

Journal publications

Risk-Aware Linear Bandits: Theory and Applications in Smart Order Routing

with Jingwei Ji and Ruihao Zhu (2023)

Accepted, Operations Research (2026) arXiv

Fast Policy Learning for Linear Quadratic Control with Entropy Regularization

with Xin Guo and Xinyu Li (2023)

Accepted, SIAM Journal on Control and Optimization (2025) SSRN

Inference of Utilities and Time Preference in Sequential Decision-Making

with Haoyang Cao and Zhengqi Wu (2024)

Accepted, Applied Mathematics and Optimization (2025) SSRN

Policy Gradient Finds Global Optimum of Nearly Linear-quadratic Control Systems

with Yinbin Han and Meisam Razaviyayn (2022)

SIAM Journal on Control and Optimization (2025) arXiv

TailGAN: Nonparametric Scenario Generation for Tail Risk Estimation

with Rama Cont, Mihai Cucuringu and Chao Zhang (2022)

Management Science (2025) arXiv Code

Model-free Analysis of Dynamic Trading Strategies

with Rama Cont and Anna Ananova (2023)

SIAM Journal on Financial Mathematics (2025) arXiv

Mean-Field Multi-Agent Reinforcement Learning: A Decentralized Network Approach

with Xin Guo, Haotian Gu and Xiaoli Wei (2021)

Mathematics of Operations Research (2024) arXiv DOI

Recent Advances in Reinforcement Learning in Finance

with Ben Hambly and Huining Yang (2021)

Mathematical Finance (2023) arXiv DOI

Policy Gradient Methods Find the Nash Equilibrium in N-player General-sum Linear-quadratic Games

with Ben Hambly and Huining Yang (2021)

Journal of Machine Learning Research (2023) arXiv Journal paper

Modelling COVID-19 Contagion: Risk Assessment and Targeted Mitigation Policies

with Rama Cont and Artur Kotlicki (2020)

Royal Society Open Science (2021) medRxiv DOI

Interbank Lending with Benchmark Rates: Pareto Optima for a Class of Singular Control Games

with Xin Guo and Rama Cont (2020)

Mathematical Finance (2021) arXiv DOI

Policy Gradient Methods for the Noisy Linear Quadratic Regulator over a Finite Horizon

with Ben Hambly and Huining Yang (2020)

SIAM Journal on Control and Optimization (2021) arXiv DOI

Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis

with Xin Guo, Haotian Gu and Xiaoli Wei (2020)

SIAM Journal on Mathematics of Data Science (2021) arXiv DOI

A General Framework for Learning Mean-Field Games

with Xin Guo, Anran Hu and Junzi Zhang (2020)

Mathematics of Operations Research (2022) arXiv DOI

Delay-Adaptive Learning in Generalized Linear Contextual Bandits

with Jose Blanchet and Zhengyuan Zhou (2020)

Mathematics of Operations Research (2022) arXiv DOI

Dynamic Programming Principles for Mean-Field Controls with Learning

with Xin Guo, Haotian Gu and Xiaoli Wei (2019)

Operations Research (2022) arXiv DOI

Transaction Cost Data Analytics for Corporate Bonds

with Xin Guo and Charles-Albert Lehalle (2019)

Quantitative Finance (2022) arXiv DOI

A Class of Stochastic Games and Moving Free Boundary Problems

with Xin Guo and Wenpin Tang (2018)

SIAM Journal on Control and Optimization (2022) arXiv DOI

Stochastic Games for Fuel Followers Problem: N versus MFG

with Xin Guo (2018)

SIAM Journal on Control and Optimization (2019) arXiv DOI

Conference proceedings

Sobolev Regularized Score Difference Estimation in Diffusion Models

with Jose Blanchet and Chenghan Xie (2026)

ICML 2026 arXiv Code

Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence

with Yinbin Han and Meisam Razaviyayn (2024)

ICML 2025 arXiv Code

Neural Network-based Score Estimation in Diffusion Models: Optimization and Generalization

with Yinbin Han and Meisam Razaviyayn (2023)

ICLR 2024 arXiv

Risk-Aware Linear Bandits with Application in Smart Order Routing

with Jingwei Ji and Ruihao Zhu (2022)

ICAIF 2022 Proceedings

Scaling Properties of Deep Residual Networks

with Alain–Sam Cohen, Rama Cont, and Alain Rossier (2021)

ICML 2021 arXiv Proceedings

Ph.D. students

I am very fortunate to advise and work with the following Ph.D. students:

Recognition & awards

Teaching

Stanford University

  • MS&E 245B: Advanced Investment Science, Winter 2026
  • MS&E 242: Machine Learning for Algorithmic Trading, Spring 2026
  • MS&E 342: Stochastic Systems and Learning Theory with Applications in Finance, Spring 2026

New York University

  • FRE-GY 9073: Stochastic Systems and Modern Machine Learning Theory (Ph.D. level), Fall 2024

University of Southern California

  • ISE 537: Financial Analytics (Machine Learning in Finance; master’s level), Fall 2021, 2022, and 2023
  • ISE 599: Special Topics in Control Theory and Reinforcement Learning (Ph.D. level), Fall 2022

University of Oxford (Tutor)

  • Stochastic Control, Hilary Term 2020
  • Machine Learning, Hilary Term 2020
  • Market Microstructure and Algorithmic Trading, Hilary Term 2020
  • Statistics and Financial Data Analysis, Michaelmas Term 2019
Berkeley
2014–2019
Oxford
2019–2021
USC
2021–2024
NYU
2024–2025
Stanford
2025–present