英文标题：
《Market Fragility, Systemic Risk, and Ricci Curvature》
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作者：
Romeil Sandhu, Tryphon Georgiou, Allen Tannenbaum
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最新提交年份：
2015
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英文摘要：
  Measuring systemic risk or fragility of financial systems is a ubiquitous task of fundamental importance in analyzing market efficiency, portfolio allocation, and containment of financial contagions. Recent attempts have shown that representing such systems as a weighted graph characterizing the complex web of interacting agents over some information flow (e.g., debt, stock returns, shareholder ownership) may provide certain keen insights. Here, we show that fragility, or the ability of system to be prone to failures in the face of random perturbations, is negatively correlated with geometric notion of Ricci curvature. The key ingredient relating fragility and curvature is entropy. As a proof of concept, we examine returns from a set of stocks comprising the S\\&P 500 over a 15 year span to show that financial crashes are more robust compared to normal \"business as usual\" fragile market behavior - i.e., Ricci curvature is a \"crash hallmark.\" Perhaps more importantly, this work lays the foundation of understanding of how to design systems and policy regulations in a manner that can combat financial instabilities exposed during the 2007-2008 crisis.
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中文摘要：
衡量金融系统的系统性风险或脆弱性是分析市场效率、投资组合配置和遏制金融传染病时一项普遍存在的具有根本重要性的任务。最近的尝试表明，将此类系统表示为一个加权图，以描述某些信息流（例如债务、股票回报、股东所有权）上交互代理的复杂网络，可以提供某些敏锐的洞察力。在这里，我们证明了脆弱性，或者说系统在面对随机扰动时容易发生故障的能力，与里奇曲率的几何概念呈负相关。与脆弱性和曲率相关的关键因素是熵。作为概念证明，我们研究了标准普尔500指数成份股在15年内的收益率，以表明金融崩溃比正常的“一切照旧”脆弱市场行为更为强劲——也就是说，里奇曲率是“崩溃的标志”也许更重要的是，这项工作为理解如何设计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。
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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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