Title: Generative Diffusion Models: Foundations and Financial Applications
Abstract: In recent years, generative AI has profoundly impacted various fields through its ability to model large-scale datasets and synthesize new content. Among these innovations, diffusion models offer a robust framework by iteratively refining noise into data, significantly enhancing the generation of high-fidelity and diverse data samples. Despite its empirical success in different domains, the theoretical foundations and systematic design of diffusion models remain largely unexplored. Furthermore, the use of diffusion models to generate dynamic data with complex structures, such as those found in financial systems, is still in an early stage.
In this talk, we will discuss the mathematical foundations of diffusion models from both optimization and generalization perspectives. We will also demonstrate how diffusion models can be applied to generate high-dimensional asset returns, addressing the curse of dimensionality by leveraging structural properties. Finally, we will briefly talk about how to incorporate domain-specific knowledge, such as volatility clustering in financial time series, to enhance the authenticity of generated data.
Bio: Renyuan Xu is an assistant professor at the Department of Finance and Risk Engineering at New York University. Previously, she was an assistant professor at the University of Southern California and a Hooke Research Fellow at the University of Oxford. She completed her Ph.D. from UC Berkeley in 2019. Her research interests include financial technology, stochastic analysis and machine learning theory. She received an NSF CAREER Award in 2024, the SIAM Financial Mathematics and Engineering Early Career Award in 2023, and a JP Morgan AI Faculty Research Award in 2022.
