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.

翻译：在金融网络违约传染防控背景下，本文研究监管机构在银行间负债与共同外部资产敞口关联的银行系统中，预先配置资本或流动性缓冲的问题。监管机构在资产价格冲击实现前，基于线性预算选择非负缓冲向量。冲击被建模为属于$\ell_{\infty}$或$\ell_{1}$不确定性集合，设计目标为：在给定压力半径下，扩大经认证的无违约/无破产区域，或最小化最坏情形清算损失。本文推导出四项精确综合结果：最大化违约韧性边际的缓冲可通过线性规划求解，并具有任一目标边际下最小预算的闭式认证表达式；最大化破产韧性边际的缓冲通过单次线性规划计算。在固定半径下，最小化最坏情形系统性损失在$\ell_{\infty}$不确定性下仍为线性规划，在$\ell_{1}$不确定性下则表现为每类资产对应一个情景块的线性规划。关键在于，在$\ell_{1}$不确定性下，精确鲁棒性仅需为每类资产增加一个线性规划块，确保计算复杂度随资产数量线性增长。推论指出最优化最坏情形损失为零时的精确预算阈值。在《Calafiore2025》的八银行基准模型、合成核心-外围网络以及基于2025年欧洲银行管理局透明度测试构建的107银行数据校准模型上的数值实验表明，该设计较均匀分配和敞口比例分配具有显著优势。实证结果同时显示：在弥散型$\ell_{\infty}$冲击下，韧性最大化与损失最小化干预策略近乎一致，但在集中型$\ell_{1}$冲击下则出现分化。