Mean Field Games, Information Design and Evolutionary Finance

平均场博弈、信息设计和进化金融

基本信息

  • 批准号:
    RGPIN-2020-06290
  • 负责人:
  • 金额:
    $ 1.89万
  • 依托单位:
  • 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

项目摘要

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)为大群体随机博弈提供了一种有用的近似方法,在这种博弈中,参与者通过经验分布相互关联。许多曾经因高维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。研究计划的一部分研究了数学金融学和经济学中出现的两个MFG问题。第一个是首席研究员之前关于基于排名的游戏和最佳奖励设计的工作的延续,我们建议着眼于带有奖励流的多阶段平均领域竞争,奖励流取决于每个阶段完成时间的排名或进程过程的运行排名。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。第二种是最优停止的MFG,玩家之间的互动既不是通过状态过程,也不是通过成本结构,至少不是通过直接的方式,而是通过停止行动所揭示的信念或信息。提出的最优停止问题包括金融事件发生的最快检测和未知市场变量值的顺序测试。通过指定每个代理人如何处理公共信息,人们可能能够分析符合公众意见对人们决策的影响,以及它是否对个人和集体都有利。该提案还包含两个新的研究方向。一种是关于随机控制和游戏,其中控制变量是由西格玛代数建模的信息,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,在金融、政治学、执法、医学测试等领域都有广泛的应用。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,可能有信息约束,以及静态信息博弈。另一条研究路线是将基于选择和突变原理的进化和学习的生物学模型纳入金融市场。这两个主题都为随机控制和数学金融领域带来了经济学和生物学等其他领域的有趣问题和想法,这将为新的理论和应用打开大门。

项目成果

期刊论文数量(0)
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会议论文数量(0)
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Zhang, Yuchong其他文献

Conditional optimal stopping: A time-inconsistent optimization
条件最优停止:时间不一致的优化
  • DOI:
    10.1214/19-aap1540
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Nutz, Marcel;Zhang, Yuchong
  • 通讯作者:
    Zhang, Yuchong
Comparison of techniques for left subclavian artery preservation during thoracic endovascular aortic repair: A systematic review and single-arm meta-analysis of both endovascular and surgical revascularization.
胸腔内主动脉修复期间左锁骨下动脉保存技术的比较:内血管和手术血运重建的系统综述和单臂荟萃分析。
  • DOI:
    10.3389/fcvm.2022.991937
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    3.6
  • 作者:
    Zhang, Yuchong;Xie, Xinsheng;Yuan, Ye;Hu, Chengkai;Wang, Enci;Zhao, Yufei;Lin, Peng;Li, Zheyun;Mo, Fandi;Fu, Weiguo;Wang, Lixin
  • 通讯作者:
    Wang, Lixin
A biomaterial-based therapy for lower limb ischemia using Sr/Si bioactive hydrogel that inhibits skeletal muscle necrosis and enhances angiogenesis.
  • DOI:
    10.1016/j.bioactmat.2023.02.027
  • 发表时间:
    2023-08
  • 期刊:
  • 影响因子:
    18.9
  • 作者:
    Yuan, Ye;Zhang, Zhaowenbin;Mo, Fandi;Yang, Chen;Jiao, Yiren;Wang, Enci;Zhang, Yuchong;Lin, Peng;Hu, Chengkai;Fu, Weiguo;Chang, Jiang;Wang, Lixin
  • 通讯作者:
    Wang, Lixin
Reward Design in Risk-Taking Contests
冒险竞赛中的奖励设计

Zhang, Yuchong的其他文献

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{{ truncateString('Zhang, Yuchong', 18)}}的其他基金

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
  • 财政年份:
    2022
  • 资助金额:
    $ 1.89万
  • 项目类别:
    Discovery Grants Program - Individual
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
  • 财政年份:
    2020
  • 资助金额:
    $ 1.89万
  • 项目类别:
    Discovery Grants Program - Individual
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:
    DGECR-2020-00373
  • 财政年份:
    2020
  • 资助金额:
    $ 1.89万
  • 项目类别:
    Discovery Launch Supplement

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Mean Field Games and Master equations
平均场游戏和主方程
  • 批准号:
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Systems, Control and Mean Field Games on Networks
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CAREER: Mean Field Games with Economics Applications: New Techniques in Partial Differential Equations
职业:平均场博弈与经济学应用:偏微分方程新技术
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CAREER: Stochastic Games on Large Graphs in the Mean Field Regime and Beyond
职业:平均场制度及其他大图上的随机博弈
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  • 财政年份:
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  • 资助金额:
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