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

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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.