Systemic Risk and Mean Field Games

点击翻译按钮获取中文摘要

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.