Time Dynamics of Systemic Risk in Banking Networks: A UEDR-PDE Approach
Bibliographic record
Abstract
Understanding the time dynamics of systemic risk in banking networks is crucial for preventing financial crises and ensuring economic stability. This paper aims to quantify key transition times in the evolution of distress within a banking system using a mathematical framework. We investigate the dynamics of systemic risk in a hypothetical, homogeneous banking network using the Undistressed–Exposed–Distressed–Recovered (UEDR) model. The UEDR model, inspired by compartmental epidemic frameworks, captures how financial distress propagates and recedes through interactions between banks. It is selected because of its tractability and its ability to distinguish between different stages of bank vulnerability. We focus on two critical times, denoted as t1 and t2, which play a fundamental role in understanding the behavior of the distressed compartment (representing the number of distressed banks) over time. The time t1 represents the first instance of a decrease in the number of distressed banks, indicating the containment of systemic risk. On the other hand, the time t2 marks the onset when the number of undistressed banks falls below a specified threshold, signifying the restoration of financial stability. We examine these time dependencies by considering the initial conditions of the UEDR model and assess their characteristics using partial differential equations. We establish the continuity, smoothness, and uniqueness of solutions for t1 and t2, along with their corresponding boundary conditions. Furthermore, we provide explicit representation formulas for t1 and t2, allowing for precise estimation when the initial population compartments are large. Our results provide practical insights for financial regulators and policymakers in determining time-sensitive interventions for mitigating systemic risk and accelerating recovery in banking systems. The findings highlight how mathematical modeling can inform real-time risk management strategies in financial networks.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".