英文标题：
《Optimal Monitoring and Mitigation of Systemic Risk in Financial Networks》
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作者：
Zhang Li, Xiaojun Lin, Borja Peleato-Inarrea, and Ilya Pollak
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最新提交年份：
2014
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英文摘要：
  This paper studies the problem of optimally allocating a cash injection into a financial system in distress. Given a one-period borrower-lender network in which all debts are due at the same time and have the same seniority, we address the problem of allocating a fixed amount of cash among the nodes to minimize the weighted sum of unpaid liabilities. Assuming all the loan amounts and asset values are fixed and that there are no bankruptcy costs, we show that this problem is equivalent to a linear program. We develop a duality-based distributed algorithm to solve it which is useful for applications where it is desirable to avoid centralized data gathering and computation. We also consider the problem of minimizing the expectation of the weighted sum of unpaid liabilities under the assumption that the net external asset holdings of all institutions are stochastic. We show that this problem is a two-stage stochastic linear program. To solve it, we develop two algorithms based on: Benders decomposition algorithm and projected stochastic gradient descent. We show that if the defaulting nodes never pay anything, the deterministic optimal cash injection allocation problem is an NP-hard mixed-integer linear program. However, modern optimization software enables the computation of very accurate solutions to this problem on a personal computer in a few seconds for network sizes comparable with the size of the US banking system. In addition, we address the problem of allocating the cash injection amount so as to minimize the number of nodes in default. For this problem, we develop two heuristic algorithms: a reweighted l1 minimization algorithm and a greedy algorithm. We illustrate these two algorithms using three synthetic network structures for which the optimal solution can be calculated exactly. We also compare these two algorithms on three types random networks which are more complex.
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中文摘要：
本文研究了向陷入困境的金融系统中最优分配现金注资的问题。在一个所有债务同时到期且资历相同的单期借贷网络中，我们解决了在节点之间分配固定金额现金以最小化未付债务加权和的问题。假设所有贷款金额和资产价值都是固定的，并且没有破产成本，我们证明了这个问题等价于一个线性规划。我们开发了一种基于二元性的分布式算法来解决这个问题，这对于需要避免集中数据收集和计算的应用程序非常有用。我们还考虑了在假设所有机构的净外部资产持有是随机的情况下，最小化未付负债加权和的期望值的问题。我们证明了该问题是一个两阶段随机线性规划。为了解决这个问题，我们在Benders分解算法和投影随机梯度下降算法的基础上开发了两种算法。我们证明，如果违约节点从不支付任何费用，则确定性最优现金注入分配问题是一个NP难的混合整数线性规划。然而，现代优化软件能够在几秒钟内在个人计算机上计算出与美国银行系统规模相当的网络规模的非常精确的解决方案。此外，我们还解决了分配现金注入量的问题，以最小化默认情况下的节点数。对于这个问题，我们开发了两个启发式算法：一个加权l1最小化算法和一个贪婪算法。我们使用三种合成网络结构来说明这两种算法，可以精确地计算出最优解。我们还比较了这两种算法在三种更复杂的随机网络上的性能。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Computer Science        计算机科学
二级分类：Social and Information Networks        社会和信息网络
分类描述：Covers the design, analysis, and modeling of social and information networks, including their applications for on-line information access, communication, and interaction, and their roles as datasets in the exploration of questions in these and other domains, including connections to the social and biological sciences. Analysis and modeling of such networks includes topics in ACM Subject classes F.2, G.2, G.3, H.2, and I.2; applications in computing include topics in H.3, H.4, and H.5; and applications at the interface of computing and other disciplines include topics in J.1--J.7. Papers on computer communication systems and network protocols (e.g. TCP/IP) are generally a closer fit to the Networking and Internet Architecture (cs.NI) category.
涵盖社会和信息网络的设计、分析和建模，包括它们在联机信息访问、通信和交互方面的应用，以及它们作为数据集在这些领域和其他领域的问题探索中的作用，包括与社会和生物科学的联系。这类网络的分析和建模包括ACM学科类F.2、G.2、G.3、H.2和I.2的主题；计算应用包括H.3、H.4和H.5中的主题；计算和其他学科接口的应用程序包括J.1-J.7中的主题。关于计算机通信系统和网络协议（例如TCP/IP）的论文通常更适合网络和因特网体系结构（CS.NI）类别。
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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