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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=741143
• 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) 为大规模随机博弈提供了有用的近似，其中玩家通过经验分布进行耦合。许多曾经因高维度而难以处理的金融和经济模型现在可以使用 MFG 方法进行分析。该研究计划的一部分研究了数学金融和经济学中出现的两个 MFG 问题。第一个是主要研究者之前关于基于排名的游戏和最佳奖励设计的工作的延续，我们建议研究多阶段平均场竞争，其奖励流取决于每个阶段的完成时间的排名阶段或进度进程的运行等级。该模型适用于许多公司或个人竞相成为第一个实现具有多个里程碑的目标的情况。第二个是最优停止的 MFG，其中参与者之间的交互既不是通过状态过程，也不是成本结构，至少不是直接的方式，而是通过停止行为所揭示的信念或信息。提出的最佳停止问题包括最快检测金融事件的发生以及顺序测试未知市场变量的值。通过详细说明每个主体如何处理公共信息，人们也许能够分析顺应民意对人们决策的影响，以及它是否对个人和集体有利。该提案还包含两个新的研究方向。一种涉及随机控制和博弈，其中控制变量是信息，由西格玛代数建模，性能标准涉及给定该信息的随机变量的条件期望。这样的问题被称为贝叶斯说服或信息设计，它在金融、政治科学、执法、医学测试等领域有着广泛的应用。我们的目标是为静态和动态信息设计问题（可能具有信息约束和静态信息博弈）开发数学理论和数值算法。另一条研究路线将基于选择和突变原理的进化和学习生物模型纳入金融市场。这两个主题都将经济学和生物学等其他领域的有趣问题和想法引入随机控制和数学金融界，这将为新的理论和应用打开大门。