Mean-field Games for Market Microstructure and Liquidity Risk

市场微观结构和流动性风险的平均场博弈

• 批准号: 1411824
• 负责人: Sergey Nadtochiy
• 金额: $ 15.3万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1411824&HistoricalAwards=false
• 关键词: Mean; field; Games; Market; Microstructure

NadtochiyDMS-1411824 Recent technological advances have created new opportunities for trading in financial markets. However, the effects of these changes are two-fold. On the one hand, they increase the competition and provide additional liquidity to the market, which, in particular, manifests itself in reduced bid-ask spreads. On the other hand, the new technology introduces opportunities for the better-equipped participants (e.g. the high-frequency traders) to adjust their positions rapidly, in order to take advantage of the trading needs of other investors. The latter may result in a sudden reduction of the market liquidity, which was well demonstrated by the so-called flash crash of 2010. As financial processes affect all parts of modern life, it is crucial for society to be able to analyze and control the financial stability of markets. The investigator develops tools for quantitative analysis of the tradeoff between the liquidity-providing role of strategic traders and the liquidity risk they generate. Such tools can be used to predict and avoid future liquidity crises, as well as to test the potential effects of new financial regulation (e.g. a transaction tax or limits on trading frequency). The investigator develops a rigorous mathematical framework for modeling market microstructure and liquidity risk by analyzing the real-world system of market participants (agents) who interact with each other through trading. The macroscopic properties of this system are described by the so-called limit order book, whose shape and dynamics arise endogenously from the actions of individual agents, rather than being taken as an input to the model. The approach is based on the methods of mean-field games, which allow for the analytically tractable description of an equilibrium in stochastic games with a large number of interacting agents. One of the challenges of the project is the complicated dependence structure between the dynamics of individual agents. For example, any realistic model of the above system requires that the agents interact through their control values, rather than through their states. This artifact introduces an additional constraint to the classical forward-backward system describing a mean-field game model, making the analysis more complicated. Another mathematical challenge is due to the fact that the control process of each agent takes values in the space of measures, which represent the limit orders submitted by the agent. As a result, the use of infinite-dimensional analysis is required to obtain an analytic characterization of the solutions to the associated optimization problems. Finally, an important problem arising in this line of study is the convergence of the proposed discrete time mean-field games to the continuous time limit. In particular, in order to address this problem, the investigator extends the existing results on discrete time approximation of the Hamilton-Jacobi-Bellman equation to the setting that allows for measure-valued controls. The project provides a natural framework for quantifying the tradeoff between the liquidity-providing role of the strategic players (e.g. the high-frequency traders) and the liquidity risk they generate. In particular, the resulting models can be used to obtain real-time predictions of the potential liquidity crises (e.g. flash crashes), as well as to test the implications of new financial regulation.

NadtochiyDMS-1411824 最近的技术进步为金融市场的交易创造了新的机会。 然而，这些变化的影响是双重的。 一方面，它们增加了竞争，为市场提供了额外的流动性，这特别表现在买卖价差的减少。 另一方面，新技术为装备较好的参与者（例如高频交易者）提供了迅速调整头寸的机会，以便利用其他投资者的交易需求。 后者可能导致市场流动性突然减少，2010年所谓的闪电崩盘就充分证明了这一点。 由于金融流程影响现代生活的各个方面，因此社会能够分析和控制市场的金融稳定性至关重要。 研究者开发工具，定量分析战略交易者提供流动性的作用和他们产生的流动性风险之间的权衡。 这些工具可用于预测和避免未来的流动性危机，以及测试新的金融监管（例如交易税或限制交易频率）的潜在影响。 研究者通过分析通过交易相互作用的市场参与者（代理人）的真实世界系统，开发了一个严格的数学框架来建模市场微观结构和流动性风险。 这个系统的宏观性质由所谓的极限订单簿描述，其形状和动力学从个体代理的行为中内生地产生，而不是作为模型的输入。 该方法是基于平均场博弈的方法，它允许在随机游戏中的平衡与大量的相互作用的代理人的分析听话的描述。 该项目的挑战之一是个体代理之间的动态复杂的依赖结构。 例如，上述系统的任何现实模型都要求代理通过其控制值而不是通过其状态进行交互。 这个人工制品引入了一个额外的约束，经典的前向-后向系统描述的平均场博弈模型，使分析更加复杂。 另一个数学挑战是由于每个代理的控制过程在度量空间中取值，度量空间代表代理提交的限价订单。 因此，需要使用无限维分析来获得相关优化问题的解的解析表征。 最后，在这条线的研究中出现的一个重要问题是所提出的离散时间平均场游戏的连续时间限制的收敛性。 特别是，为了解决这个问题，调查员扩展现有的结果离散时间近似的Hamilton-Jacobi-Bellman方程的设置，允许测量值控制。 该项目提供了一个自然的框架，用于量化战略参与者（例如高频交易者）的流动性提供角色与其产生的流动性风险之间的权衡。 特别是，由此产生的模型可以用来获得潜在的流动性危机（如闪电崩盘）的实时预测，以及测试新的金融监管的影响。