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Systemic Risk and Mean Field Games

系统性风险和平均场博弈

基本信息

批准号：
1814091
负责人：
Jean-Pierre Fouque
金额：
$ 27.38万
依托单位：
University of California-Santa Barbara
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1814091&HistoricalAwards=false
关键词：
Systemic Risk Mean Field Games

项目摘要

The banking system can be viewed as a large network of agents in interaction, entering in contracts and exposed to the risk of counter-party defaults. Systemic risk corresponds to rare events of many defaults in cascade, disrupting liquidity and the economy as a whole. This research project concerns modeling this network in interaction and studying the limiting behavior as the number of agents becomes large. The project studies Nash equilibria, whose limits are described by so-called mean field games. The focus is on the effects of time delays and randomness on the network itself. This research aims to help understand and ultimately prevent the occurrence of systemic adverse events. From the point of view of the regulators, it is important to rank institutions according to their contributions to systemic risk; on the other hand, this ranking needs to be fair to the banks. The research also aims to develop mathematical tools to measure systemic risk and design fair allocation schemes.Mathematically, systemic risk events in the network of banks correspond to a large deviation principle describing the occurrence of the small probability events in which a large number of participants are defaulting. The research consists in using mean field game theory to derive large deviation of the finite player games. The first goal is to consider the effect of delays in the game and develop the corresponding theory of mean field games with delay. The second goal is to study large deviations for games on stochastic networks. The main tool will be to use the master equation for the corresponding mean field game, specifically to explore how the stochastic nature of the network will affect the rate function in the large deviation principle. The third goal is to develop a duality approach to the systemic risk measures introduced in previous work, to ensure fairness of systemic risk allocations to the participants.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.

银行体系可以被看作是一个由相互作用的代理人组成的大型网络，它们签订合同，并面临对手违约的风险。系统性风险是指一系列罕见的违约事件，扰乱流动性和整体经济。本课题研究的是在交互中对网络进行建模，并研究智能体数量变大时的限制行为。该项目研究纳什均衡，其极限由所谓的平均场博弈描述。重点是时间延迟和随机性对网络本身的影响。本研究旨在帮助了解并最终预防全身性不良事件的发生。从监管机构的角度来看，重要的是根据机构对系统性风险的贡献对其进行排名；另一方面，这个排名需要对银行公平。该研究还旨在开发数学工具来衡量系统风险和设计公平的分配方案。在数学上，银行网络中的系统性风险事件对应于描述大量参与者违约的小概率事件发生的大偏差原理。研究内容是利用平均场博弈理论推导有限人博弈的大偏差。第一个目标是考虑延迟在博弈中的影响，并发展相应的具有延迟的平均场博弈理论。第二个目标是研究随机网络上博弈的大偏差。主要工具将是使用主方程进行相应的平均场博弈，具体探讨网络的随机性如何影响大偏差原理下的速率函数。第三个目标是为之前工作中引入的系统风险措施制定一种二元方法，以确保参与者系统风险分配的公平性。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（6）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

On fairness of systemic risk measures

论系统性风险指标的公平性

DOI：
10.1007/s00780-020-00417-4
发表时间：
2020
期刊：
Finance and Stochastics
影响因子：
1.7
作者：
Biagini, Francesca;Fouque, Jean-Pierre;Frittelli, Marco;Meyer-Brandis, Thilo
通讯作者：
Meyer-Brandis, Thilo

Deep Learning Methods for Mean Field Control Problems With Delay