A series of meetings with leading international scholars in the field of financial and actuarial mathematics
Global Seminar
In three years of its work, the Seminar has become the main highlight in the field of financial mathematics in Russia
Format: online
Language: Russian / English
Language: Russian / English
More than 50 speakers
The speakers are globally recognized scholars and industry experts
Vast geography of participants — from Los Angeles to Sydney
The Seminar is open to everyone interested in financial mathematics
The speakers are globally recognized scholars and industry experts
Vast geography of participants — from Los Angeles to Sydney
The Seminar is open to everyone interested in financial mathematics
Seminar director
Yuri Kabanov
Dr. Sci. in Phys. and Maths, Professor
Chairman of the Board of Directors
Scientific Director of the Foundation
Member of Academia Europaea
Chairman of the Board of Directors
Scientific Director of the Foundation
Member of Academia Europaea
The program for spring'25
February 15
Evgeny Burnaev
Adversarial Schrödinger Bridge Matching for Fast Generative Modeling
Topic:
15:00 (MSC)
Skoltech, Russia
The Schrödinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations.
To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds.
To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds.
February 22
Renyuan Xu
Generative Diffusion Models: Foundations and Financial Applications
Topic:
15:00 (MSC)
New York University, USA
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.
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.
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