The Spectral Topology of Global Imbalances:A Graph-Theoretic Framework for Systemic Risk in the Balance of Payments

arXiv:2602.02541v1 Announce Type: new
Abstract: Traditional balance-of-payments (BoP) analysis treats national external positions as largely idiosyncratic time series. This misses an essential structural fact: global imbalances are jointly realized on a directed, weighted network of cross-border current-account and financial claims. We propose a network-theoretic paradigm in which the world economy is a directed graph whose edge weights encode net bilateral exposures. In this setting, systemic fragility is an emergent property of the spectral topology of the global exposure matrix. We develop (i) a mathematically explicit construction of a BoP adjacency operator, (ii) a textbf{Spectral Stability Criterion} proving that the system is globally asymptotically stable if and only if the spectral radius $rho(A)