Mean Field Games, Information Design and Evolutionary Finance

平均场博弈、信息设计和进化金融

• 批准号: RGPIN-2020-06290
• 负责人: Zhang, Yuchong
• 金额: $ 1.89万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765694
• 关键词: Mean; Field; Games; Information; Design

Mean field games (MFGs) provide a useful approximation for large population stochastic games in which the players are coupled through their empirical distribution. Many financial and economic models that were once intractable due to high dimensionality can now be analyzed using the MFG approach. Part of the research proposal studies two MFG problems arisen in mathematical finance and economics. The first one is a continuation of the principal investigator's previous work on rank-based games and optimal reward design, where we propose to look at a multi-stage mean field competition with a reward stream that depends on the ranking of the completion time of each stage or the running rank of the progress process. The model applies to situations where many firms or individuals compete to be the first to achieve a goal with multiple milestones. The second one is a MFG of optimal stopping where the interaction among players is neither through the state process nor the cost structure, at least not in a direct way, but through the belief or information revealed from the action of stopping. The optimal stopping problems proposed include the quickest detection of the occurrence of a financial event and the sequential testing of the value of an unknown market variable. By specifying how each agent process the public information, one may be able to analyze the effect of conformity to the public opinion on people's decision making, and whether it benefits people individually as well as collectively. The proposal also contains two new lines of research. One is concerned with stochastic control and games where the control variable is the information, modelled by sigma-algebras, and the performance criteria involves the conditional expectation of a random variable given that information. Such a problem is known as Bayesian persuasion or information design which has seen a variety of applications in finance, politic science, law enforcement, medical testing and so on. Our goal is to develop the mathematical theory and numerical algorithm for both static and dynamic information design problems, possibly with information constraints, and static information games. The other line of research incorporates biological models of evolution and learning based on the principle of selection and mutation into the financial market. Both topics bring interesting problems and ideas from other fields such as economics and biology to the stochastic control and mathematical finance communities, which will open doors for new theories and applications.

平均场博弈（MFG）提供了一个有用的近似大人口随机博弈中的球员耦合通过他们的经验分布。许多金融和经济模型，曾经是棘手的，由于高维，现在可以使用MFG方法进行分析。研究方案的一部分研究了数理金融学和数理经济学中的两个MFG问题。第一个是延续的主要研究者以前的工作排名为基础的游戏和最优奖励设计，我们建议看看一个多阶段的平均场竞争与奖励流，取决于排名的完成时间的每个阶段或运行排名的进展过程。该模型适用于许多公司或个人竞相成为第一个实现多个里程碑目标的情况。第二种是最优停止的MFG，其中参与者之间的相互作用既不是通过状态过程也不是通过成本结构，至少不是以直接的方式，而是通过停止行为所揭示的信念或信息。提出的最优停止问题包括最快检测金融事件的发生和序列测试的价值未知的市场变量。通过指定每个代理人如何处理公共信息，人们可以分析顺应公众舆论对人们决策的影响，以及它是否有利于个人和集体。该提案还包括两个新的研究方向。一个是关注随机控制和游戏的控制变量是信息，建模的西格玛代数，和性能标准涉及的条件期望的随机变量给定的信息。我们的目标是发展静态和动态信息设计问题的数学理论和数值算法，这些问题可能具有信息约束，以及静态信息博弈。另一条研究路线将基于选择和突变原理的生物进化和学习模型纳入金融市场。这两个主题带来了有趣的问题和想法，从其他领域，如经济学和生物学的随机控制和数学金融社区，这将打开大门，新的理论和应用。