Conference: Stochastic Control for Financial Engineering: Methods and Numerics

《金融工程的随机控制：方法与数值》研讨会将于2023年6月20-23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天的研讨会将提供关于随机过程、控制和博弈的数学主题的最新技术进展的广泛但全面的概述，以及这些理论方法的许多不同应用领域。的确，除了历史上专注于金融工程的领域外，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。不可否认，这些应用是当前社会和经济挑战的核心，对它们进行定量研究有助于为公共政策提供信息。因此，这次讲习班的目的是加强数学之间的联系，特别是关于随机过程及其在上述领域的应用。我们期待这次会议将有助于启动新的跨学科合作，帮助解决当前世界面临的各种问题，并预测未来的经济和社会挑战。奖励资金将帮助支付参与者的旅费和当地费用，强调支持不同的初级研究人员群体(博士后候选人、博士后研究员和其他职业生涯早期研究人员)。更确切地说，该奖项将允许赞助大约30名初级研究人员，其中包括10名口头报告和12名海报会议。随机分析和控制理论不断发展，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。考虑到经济和金融主体之间的相互作用，还需要开发新的数学工具，特别是将平均场博弈理论落实到数学框架中。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(BSDE)理论，已经受到随机微分对策的发展的强烈影响，特别是我们可以注意到最近关于二阶、平均场或McKean-Vlasov倒向随机微分方程的结果。这个领域显然受到了我们所处的技术时代的积极影响，例如，机器学习的最新发展使我们能够以非常有效的方式以数字方式解决许多随机控制问题和游戏。但应该指出的是，反过来也是正确的：随机控制方法和技术是调查和评估高级数值方法的关键，例如深度学习或Q学习和神经网络。因此，在理论层面，讲习班将讨论随机偏微分方程和(McKean-Vlasov，二阶)倒向随机微分方程、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以应用为导向的，本研讨会还将重点关注金融应用(粗略的波动性模型，但也有加密货币和机器人咨询的较新模型)以及社会政策问题，如系统风险、流行病管理等。更多信息可在活动网站上找到：https://scfe.princeton.edu/.This奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.