报告题目：Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure
时 间：2026年5月20日（星期三）10：00
地 点：科研楼18号楼1102
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that integrates latent factor structure into generative diffusion processes, bridging econometrics with modern generative AI to address the challenges of the curse of dimensionality and data scarcity in financial simulation. By exploiting the low-dimensional factor structure inherent in asset returns, we decompose the score function--a key component in diffusion models--using time-varying orthogonal projections, and this decomposition is incorporated into the design of neural network architectures. We derive rigorous statistical guarantees, establishing nonasymptotic error bounds for both score estimation at O(d^{5/2} n^{-2/(k+5)}) and generated distribution at O(d^{5/4} n^{-1/2(k+5)}), primarily driven by the intrinsic factor dimension k rather than the number of assets d, surpassing the dimension-dependent limits in the classical nonparametric statistics literature and making the framework viable for markets with thousands of assets. Numerical studies confirm superior performance in latent subspace recovery under small data regimes. Empirical analysis demonstrates the economic significance of our framework in constructing mean-variance optimal portfolios and factor portfolios. This work presents the first theoretical integration of factor structure with diffusion models, offering a principled approach for high-dimensional financial simulation with limited data. Joint work with Minshuo Chen (Northwestern), Renyuan Xu (Stanford), and Yumin Xu (PKU).
报告人简介：张瑞勋，北京大学数学科学学院长聘副教授/研究员、金融数学系副主任。 近年研究兴趣集中在AI+Finance，入选国家海外高层次人才计划青年项目，主持教育部U40项目、国家重点研发计划青年科学家项目、国家自然科学基金面上项目等，出版专著3部，在Proceedings of the National Academy of Sciences、Management Science、Operations Research、Journal of the American Statistical Association、Mathematical Finance等国际顶尖期刊上发表论文30余篇，研究工作获标普全球ESG学术研究奖、ICPM学术研究奖、SIAM金融数学与工程最佳论文、Questrom–CEMA最佳论文、CFRI&CIRF最佳论文、INFORMS金融最佳学生论文等奖项。任Digital Finance、International Journal of Financial Engineering等期刊编委，获2025年Operations Research审稿人杰出服务奖。 2011年获北京大学数学与应用数学、经济学（双学位）学士；2015年获麻省理工学院（MIT）应用数学博士，师从Andrew W. Lo教授。