Conference: Stochastic Control for Financial Engineering: Methods and Numerics

研讨会“金融工程的随机控制：方法和数值”将于20-23年6月20日至23日在普林斯顿大学举行。通过该领域领先专家的演讲，这个为期4天的研讨会将围绕随机过程，控制和游戏以及这些理论方法的许多不同应用领域，对数学主题的最新技术进展进行广泛而全面的概述。事实上，除了历史上对金融工程的关注，现在还有许多新的应用领域，包括机器学习，金融科技，经济，金融政策和监管，疫情管理，甚至气候变化。这些应用无疑是当前社会和经济挑战的核心，以定量的方式研究它们有助于为公共政策提供信息。因此，本次研讨会的目的是加强数学之间的联系，特别是因为它涉及到随机过程及其应用到上述领域。我们希望这次会议有助于启动新的跨学科合作，这将有助于解决目前世界面临的各种问题，并预测未来的经济和社会挑战。奖金将用于支付与会者的差旅费和当地费用，重点是支持各种初级研究人员（博士）。候选人，博士后研究员和其他早期职业研究人员）。更准确地说，该奖项将允许赞助约30名初级研究人员，其中包括10名口头报告和十几名海报会议。随机分析与控制理论不断发展，最近的进展包括粗糙路径理论，最优运输，随机偏微分方程等。考虑经济和金融代理人之间的相互作用也需要开发新的数学工具，特别是将平均场博弈论纳入数学框架。作为一个例子，与随机控制相关的工具之一，即倒向随机微分方程（BSDs）理论，已经受到随机微分博弈发展的强烈影响，我们可以特别注意到最近的结果，二阶，平均场或McKean-Vlasov BSDes。该领域显然受到我们生活的技术时代的积极影响，机器学习的最新发展允许例如以非常有效的方式数值解决许多随机控制问题和游戏。但应该注意的是，反过来也是如此：随机控制方法和技术是研究和评估高级数值方法（如深度学习或Q学习和神经网络）的关键。因此，在理论层面，研讨会将讨论随机偏微分方程和（McKean-Vlasov，二阶）BSDEs，主方程和深度学习的随机方法，以及路径随机分析和签名过程。此外，由于随机控制和博弈的数学理论本质上是面向应用的，因此本次研讨会还将重点关注金融应用（粗略波动模型，以及加密货币和机器人建议的新模型）以及社会政策问题，如系统性风险，流行病管理等。更多信息可以在活动网站上找到：https://scfe.princeton.edu/.This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

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.