title: Ricci curvature: An economic indicator for market fragility and systemic risk.
abstract: Quantifying the systemic risk and fragility of financial systems is of vital importance in analyzing market efficiency, deciding on portfolio allocation, and containing financial contagions. At a high level, financial systems may be represented as weighted graphs that characterize the complex web of interacting agents and information flow (for example, debt, stock returns, and shareholder ownership). Such a representation often turns out to provide keen insights. We show that fragility is a system-level characteristic of "business-as-usual" market behavior and that financial crashes are invariably preceded by system-level changes in robustness. This was done by leveraging previous work, which suggests that Ricci curvature, a key geometric feature of a given network, is negatively correlated to increases in network fragility. To illustrate this insight, we examine daily returns from a set of stocks comprising the Standard and Poor's 500 (S&P 500) over a 15-year span to highlight the fact that corresponding changes in Ricci curvature constitute a financial "crash hallmark." This work lays the foundation of understanding how to design (banking) systems and policy regulations in a manner that can combat financial instabilities exposed during the 2007-2008 crisis.
authors.affiliation: Departments of Computer Science and Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA.
authors.forename: Romeil S
authors.initials: RS
authors.lastname: Sandhu
authors.affiliation: Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA.
authors.forename: Tryphon T
authors.initials: TT
authors.lastname: Georgiou
authors.affiliation: Departments of Computer Science and Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA.
authors.forename: Allen R
authors.initials: AR
authors.lastname: Tannenbaum
mesh_terms: D000465:Algorithms; D003132:Commerce / Q000191:economics; D006801:Humans; D018803:Models, Economic; D008962:Models, Theoretical; D012306:Risk
keywords: Complex Networks; Control; Financial Networks; Graph Theory; Ricci Curvature; Systemic Risk