论文标题
默认歧义：找到清除问题的最佳解决方案
Default Ambiguity: Finding the Best Solution to the Clearing Problem
论文作者
论文摘要
我们使用债务合同和特定银行对之间的信用违约掉期研究金融网络。鉴于这样的金融体系，我们想决定哪些银行违约，以及这些违约银行可以支付多少债务。可以很容易地解决此问题的多种解决方案，从而导致默认歧义的情况，以及为财务权威实施的一系列可能解决方案。 在本文中，我们研究了此类财务系统的解决方案空间的性质，并分析了从一组解决方案中选择的广泛合理目标功能。此类目标功能的示例包括最大程度地减少违约银行的数量，最大程度地减少未付债务的数量，最大化满意的银行的数量以及许多其他银行的数量。我们表明，对于所有这些目标，对于任何$ε> 0 $，将最佳解决方案近似于$ n^{1-ε} $ factor是NP-HARD，其中$ n $表示银行数量。此外，我们表明，从金融监管机构的角度来看，这种情况很难避免：如果我们对债务的权重，网络结构或银行必须拥有的资金数量施加强大限制，也会产生相同的硬度结果。但是，如果我们同时限制了网络结构和资金数量，则解决方案将变得唯一，并且可以有效地找到它。
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.
