An interdisciplinary team of Illinois researchers has been awarded a two-year grant from the Applied Mathematics Program at the National Science Foundation. The proposed research, led by Hal Schenck (mathematics) and Richard Sowers (industrial and enterprise systems engineering), seeks to understand systemic risk in interconnected financial networks through persistent homology, which is a tool to unfold networks and give local-to-global insights.
Written by Hal Schenck
An interdisciplinary team of Illinois researchers has been awarded a two-year grant from the Applied Mathematics Program at the National Science Foundation. The proposed research, led by Hal Schenck (mathematics) and Richard Sowers (industrial and enterprise systems engineering), seeks to understand systemic risk in interconnected financial networks through persistent homology, which is a tool to unfold networks and give local-to-global insights.
Richard Sowers“This project, ‘Systemic Risk and Topology,’ is focused on a novel application of recently developed tools in computational topology to certain problems of risk in financial networks,” explains Schenck. “Complex problems often benefit from being viewed in a new light. We're using persistent homology to study behavior of financial trading networks.”
“The world is awash in data: How can we extract meaning and understand connectivity from it?” says Sowers. “The problem of understanding interconnectedness is one of today's premier challenges. Connectivity is ubiquitous; interconnections often allow a system to be tapped to its full potential and enhance its robustness. The flip side of connectivity is that it gives rise to pathways for unexpected emergent behavior and even systemic collapse.”
One answer, as proposed by the investigators, is via the mathematical discipline of algebraic topology, which is a tool to distill the study of complex objects or spaces into a simple form.
For example, how can we distinguish between an orange and a donut? The obvious answer is that the donut has a "hole"; algebraic topology makes the natural intuition rigorous. In particular, algebraic topology is built to probe the relationship between local and global structures; this makes it an ideal tool for studying financial trading networks.
The proliferation of problems where there is a confluence of local/global transitions and a large experimental data set has given rise to the field of applied algebraic topology, yielding a systematic way to unfold connections.
“We interpret various notions of collapse of financial networks via this unfolding perspective,” Schenck added. “The work focuses on clearing networks, which encode trades and liabilities, and bring the tools developed in applied topology to bear on unfolding the interconnections in such networks. In particular, we study how local events propagate: under what circumstances does contagion and systemic collapse result from a local event?”
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Contact: Richard Sowers, Department of Industrial and Enterprise Systems Engineering, 217/333-6246.
Hal Schenck, Department of Mathematics, 217/333-2229.
If you have any questions about the College of Engineering, or other story ideas, contact Rick Kubetz, writer/editor, Engineering Communications Office, University of Illinois at Urbana-Champaign, 217/244-7716.