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

Nassim Nicholas Taleb

NYU-Tandon School of Engineering; New England Complex Systems Institute

Raphael Douady

Riskdata; CES Univ. Paris 1

November 5, 2013

Quantitative Finance, Forthcoming

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.

Number of Pages in PDF File: 19

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

JEL Classification: D81

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Date posted: August 6, 2012 ; Last revised: April 4, 2014

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: https://ssrn.com/abstract=2124595 or http://dx.doi.org/10.2139/ssrn.2124595

Contact Information

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
New England Complex Systems Institute ( email )
24 Mt. Auburn St.
Cambridge, MA 02138
United States
Raphael Douady
Riskdata ( email )
6, rue de l'Amiral Coligny
Paris, 75001
HOME PAGE: http://www.riskdata.com
CES Univ. Paris 1 ( email )
106 bv de l'Hôpital
Paris, 75013
Feedback to SSRN

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