Mathematical definition, mapping, and detection of (anti)fragility
给出了脆弱性和反脆弱性的数学定义，将其与波动性和非线性效应联系起来，并提出一种无需模型和概率的快速启发式检测方法，能识别模型错误和隐藏风险，优于压力测试等方法。
We provide a mathematical definition of fragility and antifragility as\nnegative or positive sensitivity to a semi-measure of dispersion and volatility\n(a variant of negative or positive "vega") and examine the link to nonlinear\neffects. We integrate model error (and biases) into the fragile or antifragile\ncontext. Unlike risk, which is linked to psychological notions such as\nsubjective preferences (hence cannot apply to a coffee cup) we offer a measure\nthat is universal and concerns any object that has a probability distribution\n(whether such distribution is known or, critically, unknown). We propose a\ndetection of fragility, robustness, and antifragility using a single\n"fast-and-frugal", model-free, probability free heuristic that also picks up\nexposure to model error. The heuristic lends itself to immediate\nimplementation, and uncovers hidden risks related to company size, forecasting\nproblems, and bank tail exposures (it explains the forecasting biases). While\nsimple to implement, it outperforms stress testing and other such methods such\nas Value-at-Risk.\n