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Mathematical Definition, Mapping, and Detection of (Anti)Fragility

Quantitative Finance, Forthcoming

19 Pages Posted: 6 Aug 2012 Last revised: 4 Apr 2014

Nassim Nicholas Taleb

NYU-Tandon School of Engineering

Raphael Douady

Riskdata; Stony Brook university ; CES Univ. Paris 1

Date Written: November 5, 2013


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.

Keywords: Fragility, Risk Management, Stress Testing, Model Error, Black Swans

JEL Classification: D81

Suggested Citation

Taleb, Nassim Nicholas and Douady, Raphael, Mathematical Definition, Mapping, and Detection of (Anti)Fragility (November 5, 2013). Quantitative Finance, Forthcoming. Available at SSRN: or

Nassim Nicholas Taleb (Contact Author)

NYU-Tandon School of Engineering ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

Raphael Douady

Riskdata ( email )

6, rue de l'Amiral Coligny
Paris, 75001


Stony Brook university ( email )

Stony Brook, NY 11794
United States

CES Univ. Paris 1 ( email )

106 bv de l'Hôpital
Paris, 75013

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