Systemic Risk and Mean Field Games

银行体系可以被视为一个相互作用、签订合同并面临交易对手违约风险的大型代理人网络。系统性风险相当于罕见的事件，即许多违约接踵而至，扰乱流动性和整个经济。这项研究项目涉及到在交互中对该网络进行建模，并研究当代理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来描述。重点放在时延和随机性对网络本身的影响上。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机构进行排名；另一方面，这种排名需要对银行公平。研究还旨在开发数学工具来衡量系统性风险并设计公平分配方案，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的发生的大偏差原则。研究内容在于利用平均场博弈理论推导出有限人对策的大偏差。第一个目标是考虑博弈中延迟的影响，并发展相应的带有延迟的平均场对策理论。第二个目标是研究随机网络上对策的大偏差。主要的工具将是使用相应的平均场博弈的主方程，具体探讨网络的随机性如何影响大偏差原理中的速率函数。第三个目标是对先前工作中引入的系统性风险措施制定一种双重方法，以确保对参与者的系统性风险分配的公平性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.