标题： 稀疏化默认：处于困境中的金融网络的最佳救助政策 显示英文标题

标题： Sparsifying Defaults: Optimal Bailout Policies for Financial Networks in Distress

摘要： 过去几年的事件揭示了对系统地建模和分析大型金融网络的工具的迫切需求。这类工具的许多应用包括预测系统性失败以及分析经济政策决策的可能影响。 我们研究了借款-贷款人网络中救助金额和结构的优化问题：给定系统内需要注入的固定金额现金，应该如何将其分配给节点，以实现未偿债务总额最小化或违约节点数量最小化？ 通过证明最小化未偿债务总额的问题等价于一个线性规划问题，我们开发了一个精确算法。 对于最小化违约节点数量的问题，我们使用重加权l1最小化方法开发了一个近似算法。 我们用一个可以用精确方法计算最优解的合成数据示例来说明这个算法，并通过数值模拟表明我们的算法所得出的解接近最优解。 显示英文摘要

摘要： The events of the last few years revealed an acute need for tools to systematically model and analyze large financial networks. Many applications of such tools include the forecasting of systemic failures and analyzing probable effects of economic policy decisions. We consider optimizing the amount and structure of a bailout in a borrower-lender network: Given a fixed amount of cash to be injected into the system, how should it be distributed among the nodes in order to achieve the smallest overall amount of unpaid liabilities or the smallest number of nodes in default? We develop an exact algorithm for the problem of minimizing the amount of unpaid liabilities, by showing that it is equivalent to a linear program. For the problem of minimizing the number of defaults, we develop an approximate algorithm using a reweighted l1 minimization approach. We illustrate this algorithm using an example with synthetic data for which the optimal solution can be calculated exactly, and show through numerical simulation that the solutions calculated by our algorithm are close to optimal.