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

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 network model, we extend 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 joint QUBO that simultaneously determines equilibrium failures and optimal interventions under budget constraints. To characterize the influence of individual institutions, we introduce bailout susceptibility as a response-based measure of systemic importance and develop a susceptibility-driven greedy intervention strategy. Numerical simulations demonstrate equilibrium valuation, worst-case cascade identification, optimal bailout allocation, and susceptibility analysis on financial 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 establishes a unified approach for systemic risk analysis that is compatible with classical annealing, quantum-inspired optimization, and emerging quantum annealing technologies