Серия встреч с ведущими российскими и зарубежными учеными в области финансовой и актуарной математики
ГЛОБАЛЬНЫЙ СЕМИНАР
За три года работы семинар стал ключевым событием финансовой математики в России
Формат: онлайн
Язык: русский / английский
Язык: русский / английский
Более 50 спикеров
Докладчики — ведущие мировые ученые и специалисты из индустрии
География экспертов и слушателей — от Лос-Анджелеса до Сиднея
Семинар является открытым для всех, кому интересна финансовая математика
Докладчики — ведущие мировые ученые и специалисты из индустрии
География экспертов и слушателей — от Лос-Анджелеса до Сиднея
Семинар является открытым для всех, кому интересна финансовая математика
РУКОВОДИТЕЛЬ СЕМИНАРА
Кабанов Юрий Михайлович
д.ф.-м.н., профессор
Председатель Совета директоров
Научный директор Фонда
Член Academia Europaea
Председатель Совета директоров
Научный директор Фонда
Член Academia Europaea
ПРОГРАММА ВЕСЕННЕГО семестра'25
15 | 02 | 2025
Евгений Бурнаев
Adversarial Schrödinger Bridge Matching for Fast Generative Modeling
Тема:
15:00 (МСК)
Сколтех, Россия
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.
22 | 02 | 2025
Рэньюань Сюй
Generative Diffusion Models: Foundations and Financial Applications
Тема:
15:00 (МСК)
Нью-Йоркский университет, США
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.
Предыдущие выступления
