We study financial networks where banks are connected through bilateral liabilities and may default when resources are insufficient to meet obligations. We consider both the standard proportional clearing model and a priority-proportional clearing model in which banks repay creditors according to exogenously given priority classes. In such markets, portfolio compression is a process where several banks come to a netting arrangement which reduces liabilities without changing any bank's net exposure, essentially removing cycles of debt. Our goal is to understand whether portfolio compression schemes can be designed to improve clearing outcomes for a large fraction of banks. We provide a computational characterization of the benefits and limitations of compression. On the positive side, we give a polynomial-time algorithm to compute a maximal clearing outcome under priority-proportional clearing, and we show that it is possible to decide in polynomial time whether there exists a compression that limits defaults to at most one bank. On the negative side, we show that several natural optimization and decision problems are computationally intractable: deciding whether some compression can reduce the number of defaulting banks below a given threshold, or whether a specific bank can be saved from defaulting, is $\NP$-hard even in restricted settings and under proportional clearing. We further present a mixed integer linear programming (MILP) formulation that computes a compression maximizing the number of non-defaulting banks, providing a practical approach to this hard problem. Using our MILP formulation, we perform simulations on both synthetic and real-world datasets to analyze the effects of portfolio compression.

翻译：我们研究银行通过双边负债相互关联的金融网络，当资源不足以履行义务时可能发生违约。我们同时考虑标准比例清算模型和优先级比例清算模型，在后一模型中，银行根据外生给定的优先级类别向债权人偿还债务。在此类市场中，投资组合压缩是一个过程，多家银行通过净额结算安排减少负债而不改变任何银行的净敞口，本质上消除了债务循环。我们的目标是理解能否设计投资组合压缩方案以改善大部分银行的清算结果。我们提供了压缩收益与局限性的计算刻画。在积极方面，我们给出了在优先级比例清算下计算最大清算结果的多项式时间算法，并证明可以在多项式时间内判定是否存在将违约限制在最多一家银行的压缩方案。在消极方面，我们证明若干自然优化和决策问题在计算上难解：判定是否存在某种压缩使违约银行数量低于给定阈值，或特定银行能否免于违约，即使在受限设定和比例清算下也是$\NP$-难的。我们进一步提出了一个混合整数线性规划（MILP）公式，用于计算最大化非违约银行数量的压缩方案，为这一难题提供了实用方法。基于我们的MILP公式，我们在合成数据集和真实数据集上进行了仿真，以分析投资组合压缩的效果。