（反）脆弱性的数学定义、映射和检测
Mathematical Definition, Mapping, and Detection of (Anti)Fragility
摘要：
我们提供了一个数学定义的脆弱性和反脆弱性为负或正的敏感性，分散性和波动性的半措施（一个变种的负或正的“织女星”），并检查链接到非线性效应。我们将模型误差（和偏差）整合到脆弱性或反脆弱性背景中。与风险不同，风险与主观偏好等心理概念有关（因此不能适用于咖啡杯），我们提供了一种普遍的度量，涉及任何具有概率分布的对象（无论这种分布是已知的还是关键的未知的）。我们提出了一个检测的脆弱性，鲁棒性和反脆弱性使用一个单一的“快速和节俭”，无模型，无概率启发式，也拿起暴露于模型错误。启发式有助于立即实施，并揭示与公司规模，预测问题和银行尾部风险相关的隐藏风险（它解释了预测偏差）。虽然易于实现，但它优于压力测试和其他类似方法，如风险价值。
英文摘要：
We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it outperforms stress testing and other such methods such as Value-at-Risk.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
