Ricci curvature: An economic indicator for market fragility and systemic risk.
Ricci curvature: An economic indicator for market fragility and systemic risk.
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DOI：
10.1126/sciadv.1501495
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发表时间：
2016-05
期刊：
影响因子：
13.6
通讯作者：
Tannenbaum AR
中科院分区：
文献类型：
--
作者：
Sandhu RS;Georgiou TT;Tannenbaum AR
研究者将曲率的几何概念引入到揭示系统性风险和市场脆弱性的应用中。量化金融系统的系统性风险和脆弱性对于分析市场效率、决定投资组合配置和遏制金融传染具有重要意义。在高层次上，金融系统可以表示为加权图，其表征了交互代理和信息流（例如，债务，股票回报和股东所有权）的复杂网络。这样的表述往往能提供敏锐的洞察力。我们表明，脆弱性是一个系统级的“一切照旧”的市场行为的特点，金融崩溃总是由系统级的稳健性的变化。这是通过利用以前的工作来完成的，这表明Ricci曲率是给定网络的一个关键几何特征，与网络脆弱性的增加呈负相关。为了说明这一观点，我们研究了一组股票的每日回报率，包括标准普尔500指数（S&P 500）在15年的跨度，以强调这样一个事实，即相应的变化里奇曲率构成了金融“崩溃的标志。”这项工作为理解如何设计（银行）系统和政策法规奠定了基础，以应对2007-2008年危机期间暴露的金融不稳定性。
Researchers introduce the geometric concept of curvature toward the application of uncovering systemic risk and market fragility. Quantifying the systemic risk and fragility of financial systems is of vital importance in analyzing market efficiency, deciding on portfolio allocation, and containing financial contagions. At a high level, financial systems may be represented as weighted graphs that characterize the complex web of interacting agents and information flow (for example, debt, stock returns, and shareholder ownership). Such a representation often turns out to provide keen insights. We show that fragility is a system-level characteristic of “business-as-usual” market behavior and that financial crashes are invariably preceded by system-level changes in robustness. This was done by leveraging previous work, which suggests that Ricci curvature, a key geometric feature of a given network, is negatively correlated to increases in network fragility. To illustrate this insight, we examine daily returns from a set of stocks comprising the Standard and Poor’s 500 (S&P 500) over a 15-year span to highlight the fact that corresponding changes in Ricci curvature constitute a financial “crash hallmark.” This work lays the foundation of understanding how to design (banking) systems and policy regulations in a manner that can combat financial instabilities exposed during the 2007–2008 crisis.