Budgeted Robust Intervention Design for Financial Networks with Common Asset Exposures

Paper: arXiv 2603.27274

Authors: Giuseppe C. Calafiore

Abstract

In the context of containment of default contagion in financial networks, we here study a regulator that allocates pre-shock capital or liquidity buffers across banks connected by interbank liabilities and common external asset exposures. The regulator chooses a nonnegative buffer vector under a linear budget before asset-price shocks realize. Shocks are modeled as belonging to either an $\ell_{\infty}$ or an $\ell_{1}$ uncertainty set, and the design objective is either to enlarge the certified no-default/no-insolvency region or to minimize worst-case clearing losses at a prescribed stress radius. Four exact synthesis results are derived. The buffer that maximizes the default resilience margin is obtained from a linear program and admits a closed-form minimal-budget certificate for any target margin. The buffer that maximizes the insolvency resilience margin is computed by a single linear program. At a fixed radius, minimizing the worst-case systemic loss is again a linear program under $\ell_{\infty}$ uncertainty and a linear program with one scenario block per asset under $\ell_{1}$ uncertainty. Crucially, under $\ell_{1}$ uncertainty, exact robustness adds only one LP block per asset, ensuring that the computational complexity grows linearly with the number of assets. A corollary identifies the exact budget at which the optimized worst-case loss becomes zero. Numerical experiments on the 8-bank benchmark of \cite{Calafiore2025}, on a synthetic core-periphery network, and on a data-backed 107-bank calibration built from the 2025 EBA transparency exercise show large gains over uniform and exposure-proportional allocations. The empirical results also indicate that resilience-maximizing and loss-minimizing interventions nearly coincide under diffuse $\ell_\infty$ shocks, but diverge under concentrated $\ell_1$ shocks.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides rigorous theoretical formulations for robust capital buffer allocation under uncertainty, proving exact linear programming formulations for system resilience. Empirical evaluation is demonstrated across synthetic and calibrated real-world network data (2025 EBA transparency exercise), though code availability is not explicitly specified.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimal pre-shock buffer allocation<br/>to prevent financial contagion"] --> B["Inputs: Interbank liabilities, asset exposures,<br/>linear budget, & uncertainty sets (ℓ₁ / ℓ∞)"]
    B --> C["Optimization Formulations:<br/>Default/Insolvency Resilience & Loss Minimization"]
    C --> D["Exact Synthesis via Linear Programming<br/>(Scalable: ℓ₁ adds only 1 LP block per asset)"]
    D --> E["Validation: Experiments on 8-bank benchmark,<br/>Core-Periphery, & 107-bank EBA 2025 dataset"]
    E --> F["Key Findings: LP interventions outperform heuristics;<br/>Loss-min & Resilience-max diverge under ℓ₁ shocks"]

Cited References (20)

1. Robust Financial Networks (2024) — link
2. Default robustness and worst-case losses in financial networks — → 2403.10631
3. Interbank Asset-Liability Networks with Fire Sale Management (2023) — link
4. The Optimal Bailout Policy in an Interbank Network (2022) — link
5. Clearing Payments in Dynamic Financial Networks (2022) — link
6. Optimal Clearing Payments in a Financial Contagion Model (2021) — link
7. Computation of Systemic Risk Measures: A Mixed-Integer Programming Approach (2019) — link
8. Contagion in Financial Networks: A Threat Index (2018) — link

1 of 20 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.