BECS: Rare Systematic Risk in Markets: Modelling, Theory and Computation

这是一个探索性的建议，旨在了解金融系统中复杂性和罕见事件之间的相互作用。具体来说，我们试图为中央对手方和银行的行为建模。这种系统中的罕见事件通常来自系统各部分之间的相互作用。我们将使用大偏差和非合作博弈论的工具来描述系统风险和特殊风险如何通过高维金融系统的非线性传播的各个方面。本建议的重点是两个问题，这两个问题突出了几个典型金融体系中复杂性的几个方面。我们尤其对中央对手方和银行感兴趣。我们希望研究的复杂性是影响金融系统的各种风险，以及它们之间的（非线性）反馈。我们研究这些问题的动机是为了理解和控制金融崩溃的途径。据推测，监管要求使金融崩溃变得罕见。在这些与金融危机或市场崩溃相对应的罕见配置中，哪些是“最”可能的？我们如何才能有效地模拟这些场景？此外，我们是否可以控制系统并设计合适的市场机制，以便在崩溃发生时，最有可能以某种“首选”方式发生？这一分析的一个内在部分是金融体系固有的非合作性质；它们涉及大量的代理商，每个代理商都寻求自己的利润最大化。当考虑相关的控制问题时，我们观察到大量的智能体导致高维问题，而高维问题往往是难以解决的。我们打算研究是否可以使用平均场近似来获得聚合行为的表征。此外，我们的重点是这种结构对罕见事件的影响。系统的不同部分之间相互竞争的相互作用意味着，系统的行为通常不能仅仅通过观察系统的一部分来完全理解。

This is an exploratory proposal which seeks to understand the interaction between complexity and rare events in financial systems. Specifically, we seek to model the behavior of central counterparties and banks. Rare events in such systems often come from interaction between various parts of the system. We will use the tools of large deviations and noncooperative game theory to characterize various aspects of how systemic and idiosyncratic risk propagate through nonlinearities in high-dimensional financial systems.The focus of this proposal is on two problems which highlight several aspects of complexity in several exemplary financial systems. In particular, we are interested in central counterparties and banks. The complexity which we wish to investigate is the variety of risks which can affect financial systems, and the (nonlinear) feedbacks between them. Our motivation in these problems is to understand and control pathways of financial collapse. Assumedly, regulatory requirements make financial collapse rare. Amongst these rare configurations corresponding to financial meltdown or market collapse, which ones are the ``most'' likely? How can we efficiently simulate these scenarios? Furthermore, can we control the system and design suitable market mechanisms so that meltdown, if it occurs, is most likely to occur in some ``preferred'' way? An intrinsic part of this analysis is the inherently noncooperative nature of financial systems; they involve a large number of agents, each of whom seeks to maximize its own profit. When considering the associated control problem, we observe that the large population of agents leads to high dimensional problems that may often be intractable. We intend to examine whether mean-field approximations may be employed to obtain a characterization of aggregate behavior. Additionally, Our focus is the impact of this structure on rare events. The competing interactions between the different parts of the system imply that the behavior of the system cannot in general be fully understood by looking solely at a part of the system.