Governmental decisions regarding bailouts of strategically important companies, especially large banks, are crucial for maintaining financial system stability. The interconnectedness of financial institutions means systemic risk cannot be assessed individually; interactions between institutions significantly influence overall dynamics. Regulatory bodies like the US Financial Stability Oversight Council and the European Systemic Risk Board work to identify, monitor, and mitigate systemic risk, constantly seeking new methodologies to improve their understanding of financial crises. Examples like the UK government's bailout of the Royal Bank of Scotland in 2008–2009, while stabilizing the system, resulted in substantial taxpayer costs. The COVID-19 pandemic further highlighted the challenges of such decisions. A network model is essential for analyzing systemic risk, where nodes represent financial institutions and links represent mutual exposures, allowing the study of how distress spreads. While extensive literature exists on governmental interventions, few quantitatively assess bailout convenience from the taxpayers' perspective. This study fills this gap by proposing a framework that (a) allows for preventive actions before network compromise; (b) focuses on minimizing taxpayer losses, irrespective of overall system wealth; and (c) models government control via capital injections at each time step.

The literature on financial systemic risk and governmental interventions is vast. Network science techniques have been successfully applied to analyze network resilience and systemic risk, modeling the contagion mechanism between financial institutions through direct and indirect losses from cross-ownership and asset fire sales. Studies have investigated various aspects of government interventions, including post-bailout bank performance, effects on underwriting and market discipline, and the interplay between bailouts, bank risk profiles, and national regulation. However, few studies quantitatively assess the convenience of bailouts from the taxpayers' standpoint, which is the primary focus of this research. Existing models often optimize functions based on social costs or system wealth, neglecting the specific interests of taxpayers. This paper uniquely focuses on minimizing taxpayer losses while allowing for government control of the dynamic network via capital injections at every time step.

The proposed framework comprises three components: (1) a dynamic network model of the financial system describing contagion; (2) a set of allowed government interventions (capital investments in distressed banks); and (3) a quantitative assessment of government actions using AI techniques. Contagion is modeled as an increase in the probability of default (PD) of banks with claims on failed institutions. Government investments decrease the PD. The PD is modeled using Merton's credit risk model, allowing for both positive (investments) and negative (defaults) shocks. Simultaneous defaults are modeled using a Gaussian latent variable model. The evolution of the controlled network is simulated using multi-period Monte Carlo simulations. The system's evolution is framed as an MDP where government investments are actions and losses are negative rewards. The MDP is challenging to solve due to the complexity of the state definition, the low probability of reward signals, and the vast number of successor states. The researchers developed an AI technique, a variation of the Fitted Value Iteration algorithm, to address these challenges. This technique involves a specific value function parameterization, a learning process backward in time, and a duality between network dynamics and MDP rewards to reduce computational complexity. The algorithm assesses the optimality of government decisions and determines the optimal actions for each time step and network state. This model quantifies the "convenience to intervene", comparing the optimal action value with the value of inaction (no investment).

The primary finding is a mathematical framework allowing governments to assess and optimize bailout decisions from a taxpayer's perspective. Using both a synthetic network (Krackhardt kite graph) and a real network of European global systemically important institutions (EBA network), the researchers analyzed the model's implications. In the Krackhardt Kite network study, they explored how bailout decisions depend on node centrality and pre-existing investments. Results showed that investing in central nodes is generally better than peripheral nodes, but that prior investment creates moral hazard, leading to a preference for continued investment in previously-bailed-out banks, even peripheral ones. The optimal action value decreases (losses decrease) as time to the end of the crisis decreases. In the EBA network study, the researchers found that government interventions only improve the expected loss if the percentage (α) of wealth loss upon default exceeds a critical threshold (αc). This threshold is endogenously determined and decreases as network distress increases. The convenience to intervene increases with longer crisis horizons, lower bank resilience (equity), and higher credit exposures. Sensitivity analysis revealed that the optimal action value function decreases with increasing discount factors, probabilities of default, and credit exposures. A critical α value separates regimes of favorable and unfavorable interventions, with this threshold decreasing in severely distressed networks. Optimal investment amount decreases with lower initial capital. Investing the minimum possible amount is consistently the worst strategy.

The findings address the research question of how to optimally manage financial systemic risk using bank bailouts, focusing on minimizing taxpayer losses. The model demonstrates that bailout decisions should not be based solely on network centrality or individual bank characteristics but on a comprehensive assessment of network-wide dynamics, taxpayer stakes, and the risk of moral hazard. The identification of a critical α threshold signifies the importance of considering the potential cost of bank failures relative to the cost of bailouts. The model's insights are directly relevant to central banks and governments, offering a quantitative tool for making informed bailout decisions, evaluating past interventions, and learning from experience. The model's ability to account for the dynamic nature of financial networks and the interplay between governmental interventions and market responses offers a valuable contribution to the field of financial risk management.

This paper contributes a novel mathematical framework and AI-based methodology for quantitatively assessing and optimizing bank bailout decisions to minimize taxpayer losses. The model highlights the importance of considering taxpayer stakes, network structure, and the risk of moral hazard. Future research could incorporate additional stochasticity to model post-crisis market conditions, allowing for optimization of the sale timing and price of acquired shares. Further extensions could consider action-dependent crisis durations.

The model's accuracy depends on the accuracy of input data, particularly the network of bilateral exposures and banks' probabilities of default. The assumption of a single regulator accountable to all European taxpayers simplifies the real-world complexities of national regulations and political considerations. The model's focus on minimizing taxpayer losses might not fully capture the broader societal impacts of financial crises.