Conference: Stochastic Control for Financial Engineering: Methods and Numerics

“金融工程的随机控制：方法和数字”研讨会将于2023年6月20日至23日在普林斯顿大学举行。通过由该领域领先专家的演讲，这个为期4天的研讨会将提供一个广泛而全面的概述，围绕随机过程，控制和博弈的数学主题的最新技术进展，以及这些理论方法的许多不同应用领域。事实上，除了历史上对金融工程的关注之外，现在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，以定量的方式研究它们可以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，特别是与随机过程有关的数学及其在上述领域的应用。我们期待这次会议有助于发起新的跨学科合作，以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。奖励资金将用于支付参与者的旅行和当地费用，强调对不同群体的初级研究人员（博士候选人，博士后研究员和其他早期职业研究人员）的支持。更确切地说，该奖项将允许资助大约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。随机分析与控制理论在不断发展，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。考虑经济和金融主体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实施到数学框架中。作为一个例子，与随机控制相关的工具之一，即后向随机微分方程（BSDE）理论，受到随机微分对策发展的强烈影响，我们可以特别注意到二阶，平均场或McKean-Vlasov BSDEs的最新结果。该领域显然受到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允许以非常有效的方式用数字解决许多随机控制问题和游戏。但应该注意的是，反过来也是正确的：随机控制方法和技术是调查和评估高级数值方法（如深度或q -学习和神经网络）的关键。因此，在理论层面，研讨会将以随机偏微分方程和（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的讲座和讨论为特色。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，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咨询的新模型）以及系统风险、流行病管理等社会政策问题。更多信息可以在活动网站上找到：https://scfe.princeton.edu/.This该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，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.