默认歧义：寻找清算问题的最佳解决方案
Default Ambiguity: Finding the Best Solution to the Clearing Problem
摘要：
我们研究特定银行对之间的债务合同和信用违约互换的金融网络。在这样一个金融体系下，我们想决定哪些银行违约，这些违约银行能偿还多少债务。这个问题很容易有多种不同的解决方案，导致违约不明确的情况，以及金融机构实施的一系列可能的解决方案。本文研究了这类金融系统的解空间的性质，并分析了从解集中选择的各种合理的目标函数。这样的目标函数的例子包括最小化违约银行的数量，最小化未偿还债务的数量，最大化满意银行的数量，等等。我们发现，对于所有这些目标，它是NP-难的近似最优解的$n^{1-ε}$因子的任何$ε>0$，与$n$表示的银行数量。此外，我们表明，这种情况是很难避免从金融监管机构的角度来看：同样的硬度结果也持有，如果我们施加强有力的限制的权重的债务，网络的结构，或银行必须拥有的资金量。然而，如果我们同时限制网络结构和资金量，那么解决方案就变得唯一，并且可以有效地找到它。
英文摘要：
We study financial networks with debt contracts and credit default swaps between specific pairs of banks. Given such a financial system, we want to decide which of the banks are in default, and how much of their liabilities can these defaulting banks pay. There can easily be multiple different solutions to this problem, leading to a situation of default ambiguity, and a range of possible solutions to implement for a financial authority. In this paper, we study the properties of the solution space of such financial systems, and analyze a wide range of reasonable objective functions for selecting from the set of solutions. Examples of such objective functions include minimizing the number of defaulting banks, minimizing the amount of unpaid debt, maximizing the number of satisfied banks, and many others. We show that for all of these objectives, it is NP-hard to approximate the optimal solution to an $n^{1-ε}$ factor for any $ε>0$, with $n$ denoting the number of banks. Furthermore, we show that this situation is rather difficult to avoid from a financial regulator's perspective: the same hardness results also hold if we apply strong restrictions on the weights of the debts, the structure of the network, or the amount of funds that banks must possess. However, if we restrict both the network structure and the amount of funds simultaneously, then the solution becomes unique, and it can be found efficiently.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
