Grant: Discovery Grants Program - Individual

Sophisticated mathematics revolutionized the financial industry. However a concomitant sophistication in the quantitative methods employed in its regulation has yet to materialize. Indeed, many of the most common regulatory tools designed to ensure financial stability remain quite blunt. Furthermore, these tools were recently demonstrated to be ineffective at preventing systemic collapse and decisions regarding who was ultimately deemed ""too big to fail"" remain controversial. Broadly speaking, the goal of the proposed research program is to address, from a mathematical perspective, problems faced by those tasked with safeguarding the stability of our financial system.The failure of a single financial institution propagates distress via the complex network of interbank borrowing and lending. The potential for such ""financial contagion"" poses a grave danger to the stability of the system, however at the present time our theoretical understanding of this phenomenon is quite limited. This is compounded by the fact that financial crises in developed nations are (thankfully) quite rare, limiting the availability of relevant empirical data.The phenomenon of financial contagion is akin to the spread of infectious diseases, where the well-developed theory of networks and random graphs has proven enormously useful with respect to modeling and simulation. A major portion of the proposed program is to explore the potential for network-based modeling and analysis of financial stability. Particular emphasis will be placed on developing quantitative tools for understanding contagion within the financial sector, the development and analysis of various ""early warning systems"" and tools for identifying institutions or clusters of institutions posing the greatest systemic threat.