📈 economics

Macroprudential Policies and Financial Stability: A Quantitative Assessment of Strategies to Mitigate Systemic Risk in Banking Networks

This paper enhances the UEDRL compartmental framework with an optimal control scheme to quantitatively demonstrate that early, coordinated macroprudential interventions effectively mitigate systemic risk by reducing distressed nodes, breaking contagion chains, and accelerating financial network recovery.

Original authors: Hamza CHERRAT, Meriem Alkama, Hiba Arif, Omar Zakary, Taj Tilila

Published 2026-08-11

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CC BY 4.0

Original authors: Hamza CHERRAT, Meriem Alkama, Hiba Arif, Omar Zakary, Taj Tilila

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the global banking system not as a collection of vaults and ledgers, but as a giant, bustling city where every building is connected by invisible bridges. In this city, if one building catches fire, the flames don't just stay there; they jump across the bridges to the next building, and then the next, potentially turning a small spark into a city-wide inferno. This is the scary reality of "systemic risk." For decades, regulators have tried to put out these fires by checking each building individually, making sure every single one has a fire extinguisher. But this approach misses the point: it's the bridges themselves that spread the danger. To understand how to stop the fire, scientists have started borrowing ideas from epidemiology—the study of how diseases spread. Just as a virus moves from a healthy person to an exposed one, then to a sick one, financial trouble can move from a healthy bank to an exposed one, then to a distressed one. The big question for the modern world is: How do we stop the financial "virus" from taking down the whole city, and what is the best way to use our limited resources (like emergency funds) to do it?

This is exactly the puzzle tackled by Hamza Cherrat and his team in their new research. They built a digital simulation of a banking city using a model they call UEDRL, which stands for Undistressed (healthy), Exposed (at risk), Distressed (sick), Recovered (healed), and Liquidated (gone forever). Think of it as a video game where you can watch the "infection" of financial trouble spread through the network. But instead of just watching the disaster unfold, the authors added a "smart controller"—a mathematical brain that acts like a super-regulator. This controller's job is to decide the perfect moment and intensity to pull three specific levers: cutting off the dangerous bridges between banks, pumping money into sick banks to help them heal, and quickly closing down banks that are too far gone to save.

The researchers ran their simulation through three different "worlds": a moderate-risk scenario (like Morocco), a highly connected scenario (like the Euro Zone), and a worst-case "Systemic Crisis" scenario (similar to the 2008 crash). In the world without any intervention, the simulation showed the financial distress spreading wildly, with a huge number of banks getting sick and eventually collapsing. However, when the smart controller stepped in, the results were dramatic. In the moderate scenario, the number of distressed banks dropped from 8% down to just 0.15%. Even in the worst-case crisis scenario, where the system was on the brink of total collapse, the controller managed to stabilize the network, drastically reducing the number of failures.

The study suggests that the most effective strategy isn't just one magic bullet, but a coordinated dance of three moves. The first and most powerful move was "interconnection reduction" (u1), which is like temporarily closing the bridges between buildings to stop the fire from jumping. The second move was "resolution programs" (u3), which involves quickly and cleanly removing the buildings that are already burning down so they don't drag others down with them. Interestingly, the simulation showed that simply adding more money (recapitalization, or u2) was less effective on its own compared to cutting the connections and managing the exits. The authors found that acting early and aggressively was key; the sooner the controller pulled the levers, the less it cost the economy in the long run. In fact, in their most severe crisis simulation, the intervention actually resulted in a net economic benefit, proving that spending money to stop the panic is cheaper than letting the panic run its course.

Ultimately, this paper doesn't claim to have solved the mystery of financial crises forever, but it provides a powerful new map for how to fight them. It suggests that treating banks like isolated islands is a mistake; they are a connected ecosystem. By using mathematical tools to find the perfect timing and mix of cutting connections, helping the sick, and removing the dead weight, regulators can turn a potential city-wide inferno into a manageable, contained incident. The simulation shows that with the right strategy, we can keep the banking city standing, even when the winds of crisis start to blow.

Technical Summary: Macroprudential Policies and Financial Stability

Problem Statement
The paper addresses the critical challenge of managing systemic risk within highly interconnected banking networks. Traditional microprudential approaches, which focus on the risk profiles of isolated institutions, are deemed structurally inadequate for capturing the collective propagation dynamics of financial shocks. The authors argue that interbank linkages can amplify individual vulnerabilities into network-wide crises through balance sheet cross-exposures, liquidity interdependencies, and shared market obligations. A significant gap exists in the literature: while network studies identify contagion pathways, they often lack the formal integration of macroprudential policy instruments. Furthermore, research combining multi-state compartmental models with advanced optimal control theory to analyze the trade-offs of state interventions remains sparse.

Methodology
To address these gaps, the authors construct an integrated framework that couples a five-state compartmental model with an optimal control problem.

The UEDRL Compartmental Model:
The study extends the existing UEDR (Undistressed-Exposed-Distressed-Recovered) framework by adding a "Liquidated" compartment, creating the UEDRL model. This model classifies the banking population $N(t)$ into five distinct states:
- U (Undistressed): Sound banks susceptible to contagion.
- E (Exposed): Banks exposed to shocks but not yet in critical distress.
- D (Distressed): Banks facing severe solvency or liquidity difficulties, acting as primary sources of contagion.
- R (Recovered): Banks that have regained stability through internal mechanisms or intervention.
- L (Liquidated): Banks that have permanently exited the system due to insolvency.
The dynamics are governed by a system of nonlinear differential equations describing transitions between these states based on contagion rates ( $\beta$ ), recovery rates ( $\alpha, \gamma_1$ ), deterioration rates ( $\sigma$ ), and liquidation rates ( $\gamma_2$ ).
Optimal Control Formulation:
The regulatory intervention is modeled as an optimal control problem aiming to minimize a cost function $J$ . This function balances three objectives:
- Minimizing the number of distressed banks ( $D$ ).
- Minimizing the economic cost of the crisis.
- Minimizing the fiscal cost of government interventions.
Three control variables are introduced:
- $u_1(t)$ : Measures to reduce interconnection/contagion (e.g., limiting exposures).
- $u_2(t)$ : Recapitalization efforts to support distressed banks.
- $u_3(t)$ : Resolution programs to liquidate non-viable banks.
The optimization utilizes Pontryagin's Maximum Principle to derive the adjoint system and characterize the optimal controls. The existence of an optimal solution is established based on the convexity of the integrand and the Lipschitz property of the state system.
Numerical Simulation:
The model is implemented in Python using a forward-backward sweep algorithm with a fourth-order Runge-Kutta integration scheme. The study calibrates parameters based on historical data from Bank Al-Maghrib and the ECB (2000–2025) and simulates three distinct scenarios:
- Morocco Scenario (2022–2025): Post-COVID conditions with moderate connectivity.
- Euro Zone Scenario (2022–2025): High interconnectivity.
- Systemic Crisis Scenario: Extreme contagion conditions similar to the 2008 crisis.

Key Results
Numerical simulations demonstrate that early and coordinated macroprudential interventions significantly alter the trajectory of financial crises:

Mitigation of Distress: Optimal control strategies markedly reduce the fraction of distressed nodes. In the Morocco scenario, the proportion of distressed banks decreased from an initial 8% to 0.15%. In the Euro Zone scenario, despite higher initial contagion, the system converged to a stable state with only 0.14% distressed banks.
Accelerated Recovery: The implementation of controls accelerates the transition of banks from the distressed ( $D$ ) to the recovered ( $R$ ) and undistressed ( $U$ ) states.
Control Activation Patterns:
- Interconnection Reduction ( $u_1$ ): Identified as the most effective tool for containing systemic contagion, with activation levels reaching 78.2% in moderate scenarios and 95.1% in crisis scenarios.
- Resolution Programs ( $u_3$ ): Played a complementary and crucial role, particularly in eliminating non-viable banks.
- Recapitalization ( $u_2$ ): Was utilized less frequently, suggesting a secondary role in immediate crisis management compared to containment and resolution.
Cost-Benefit Analysis: The objective function $J$ yielded a negative value (-2.241) in the Systemic Crisis scenario, indicating a net economic benefit from intensive early interventions compared to the costs of inaction.

Significance and Claims
The paper claims to provide a quantitative decision-support framework capable of identifying optimal intervention strategies to mitigate systemic contagion. Its primary contributions are:

Model Expansion: Extending the macro-epidemiological framework to capture irreversible defaults via the liquidation compartment.
Theoretical Integration: Mathematically formulating regulatory policy trade-offs via Pontryagin's principle within a five-state banking model.
Quantitative Validation: Demonstrating through simulation that prompt, well-coordinated intervention by supervisory bodies is essential to minimize the total economic burden of banking crises.

The authors conclude that the contagion rate is the most influential parameter affecting stability and that preventive, timely interventions generate significantly greater benefits than delayed measures. They assert that policy frameworks combining preventive actions, recapitalization, and resolution mechanisms are superior to isolated interventions, offering a promising approach for enhancing financial stability and mitigating systemic vulnerabilities.

Technical Summary: Macroprudential Policies and Financial Stability

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