Conference: Stochastic Control for Financial Engineering: Methods and Numerics

Princeton University, Princeton NJ

Investigators

Abstract

The workshop "Stochastic Control for Financial Engineering: Methods and Numerics" will be held at Princeton University from June 20-23, 2023. Through presentations by leading experts in the field, this 4-day workshop will provide a broad but thorough overview of recent technical advances in mathematical topics around stochastic processes, control, and games, as well as many different application areas of these theoretical approaches. Indeed, beyond the historical focus on financial engineering, there are now many new fields of application, including machine learning, fintech, economic, financial policy and regulation, epidemic management, and even climate change. These applications are undeniably at the heart of current social and economic challenges and studying them in a quantitative way can contribute to informing public policy. The objective of this workshop is therefore to strengthen the links between mathematics, especially as it pertains to random processes and its applications to the above-mentioned areas. We expect this meeting to help initiate new interdisciplinary collaborations that will help tackle various issues currently facing the world and anticipate future economical and societal challenges. The award funds will help defray travel and local expenses of the participants, emphasizing the support of a diverse group of junior researchers (Ph.D. candidates, postdoctoral fellows and other early-career researchers). More precisely, the award will allow to sponsor approximately 30 junior researchers, including 10 for oral presentations and a dozen for poster sessions. The theory of stochastic analysis and control is constantly developing, and recent advances include, among others, rough paths theory, optimal transport, stochastic partial differential equation and more. Considering the interactions between economic and financial agents has also required the development of new mathematical tools, and in particular the implementation of the mean field game theory into the mathematical framework. As an illustration, one of the tools associated with stochastic control, namely the Backward Stochastic Differential Equations (BSDE) theory, has been strongly impacted by the development of stochastic differential games, and we can particularly notice recent results on second-order, mean field or McKean-Vlasov BSDEs. The field is obviously positively impacted by the technological era in which we live, and recent developments in machine learning allow for example to numerically solve many stochastic control problems and games in a very efficient way. But it should be noted that the reverse is also true: stochastic control methods and techniques are key to the investigation and assessment of advanced numerical approaches such as deep or Q–learning and neural networks. Hence, at the theoretical level, the workshop will feature talks and discussions on stochastic PDEs and (McKean–Vlasov, second-order) BSDEs, stochastic approaches to the master equation and to deep learning, as well as pathwise stochastic analysis and signature processes. Furthermore, as the mathematical theory of stochastic control and games is, by nature, application-oriented, this workshop will also have a strong focus on applications to finance (rough volatility models, but also newer models for cryptocurrencies and robot advising) as well as social policy issues such as systemic risk, epidemic management, among others. More information can be found on the event website: https://scfe.princeton.edu/. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.