报告人：张瑞勋，北京大学数学科学学院金融数学系主任，研究员/长聘副教授

报告时间：2026年11月3日18：30-20：00

报告地点：览秀楼105   #腾讯会议：362-683-9628

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 and generated distribution, 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金融数学系主任，研究员/长聘副教授，统计科学中心、大数据分析与应用技术国家工程实验室、数量经济与数理金融教育部重点实验室成员。任Mathematical Finance、Digital Finance等期刊副主编。 研究兴趣包括数理金融、金融统计与机器学习，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、Operations Research、Management Science、Journal of the American Statistical Association、Mathematical Finance等国际顶尖期刊上发表论文40余篇，研究工作近5年获INFORMS和SIAM等国际最佳论文奖7项，获2025年Operations Research审稿人杰出服务奖。与中国人民银行、谷歌、高盛和若干量化投资企业有丰富的合作和应用落地经验。 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。