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Budgeted Robust Intervention Design for Financial Networks with Common Asset Exposures

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.

Budgeted Robust Intervention Design for Financial Networks with Common Asset Exposures

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 or an 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 uncertainty and a linear program with one scenario block per asset under uncertainty. Crucially, under 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 shocks, but diverge under concentrated shocks.

Paper Structure

This paper contains 14 sections, 8 theorems, 24 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Model and Problem Formulation
  3. Clearing and systemic loss
  4. Resilience-Optimal Buffer Design
  5. Default resilience margin
  6. Insolvency resilience margin
  7. Loss-Optimal Buffer Design
  8. $\ell_\infty$-bounded perturbations
  9. $\ell_1$-bounded perturbations
  10. Numerical Examples
  11. Eight-node benchmark
  12. Synthetic 353-node core-periphery network
  13. Data-backed 107-bank EBA calibration
  14. Conclusions

Key Result

Proposition 1

For any fixed $b\in\mathbb{R}^n_+$, Hence $\epsilon_{\mathrm{def}}(b)$ is the largest shock radius for which every $\delta\in\mathcal{U}_p(\epsilon)$ yields full clearing $p=\bar{p}$.

Figures (3)

  • Figure 1: Eight-node benchmark. Optimal intervention dominates simple heuristics for both resilience maximization and loss minimization.
  • Figure 2: Data-backed 107-bank EBA calibration. Diffuse $\ell_\infty$ shocks make margin-optimal and loss-optimal designs nearly coincide, whereas concentrated $\ell_1$ shocks separate the two objectives.
  • Figure 3: Synthetic 353-node core-periphery network. At $\epsilon=0.04$, topology-aware loss-optimal design markedly outperforms margin-optimal and uniform allocations.

Theorems & Definitions (18)

  • Proposition 1
  • Theorem 1
  • proof
  • Remark 1
  • Corollary 1
  • proof
  • Theorem 2
  • proof
  • Remark 2
  • Theorem 3
  • ...and 8 more