Financial Contagion Networks as Annealing-Ready Ising Systems Cascades, Bailout Optimization, and Susceptibility

RESUMO

Interconnected financial systems are vulnerable to cascading failures arising from cross-holdings and nonlinear contagion, making the analysis and mitigation of systemic risk a challenging computational problem. In this work, we develop a unified optimization framework for financial network analysis based on Ising models and Quadratic Unconstrained Binary Optimization (QUBO). Starting from the Elliott Golub Jackson financial model, we extend the equilibrium valuation to incorporate threshold-induced failures, formulate the Maximum Cascade Failure Problem, and derive an equivalent QUBO representation. We then formulate the Optimal Bailout Allocation Problem as a controlled Ising model and transform the resulting bi-level optimization into a single QUBO that simultaneously determines optimal equilibrium and interventions under budget constraints. To characterize the influence of individual institutions, we introduce a bailout susceptibility measure and response-based importance measure and develop a susceptibility-driven greedy intervention strategy. Numerical simulations demonstrate optimal valuation, worst-case cascade identification, bailout allocation, and scalability across networks of varying sizes. Beyond optimization, the Ising representation provides a general statistical-mechanical framework for analyzing financial contagion, enabling the application of response theory, Monte Carlo methods, and other techniques developed for interacting spin systems. The proposed framework is compatible with classical annealing, quantum-inspired optimization, and emerging quantum annealing technologies.