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This article aims at providing a proper mathematical definition of fragility, robustness, and antifragility and examining how these apply to different cases where this notion is applicable. Intrinsic and Inherited Fragility: Our definition of fragility is two-fold.
- Nassim Nicholas Taleb, Raphaël Douady
- 2013
Strictly speaking, a fragility function displays the conditional probability of failure for a component or a system, for given intensity values, accounting for uncertainty in capacity as well as demand. Figure 1 visualizes such a fragility function with F=failure and im=intensity.
What does it mean for a solution to a system of differential equations to be fragile? A context for the term can be found here: This is taken from here in Mathematical Methods for Mechanics: A Handbook With MATLAB Experiments by Eckart Gekeler. Does it mean it is small perturbations grow over time?
Intrinsic and Inherited Fragility: Our definition of fragility is twofold. First, of concern is the intrinsic fragility, the shape of the probability distribution of a variable and its sensitivity to s‒, a parameter controlling the left side of its own distribution.
The list below has some of the most common symbols in mathematics. However, these symbols can have other meanings in different contexts other than math.
SymbolNameRead AsMeaning=Equalis equal toIf x=y, x and y represent the same value ...≡Definitionis defined asIf x≡y, x is defined as another name of ...≈Approximately equalis approximately equal toIf x≈y, x and y are almost equal.≠Inequationdoes not equal, is not equal toIf x≠y, x and y do not represent the same ...Aug 6, 2012 · 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.
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Apr 14, 2021 · Fragility functions are resulted from a structural assessment of the system (in the case of analytical form). In simple language, the fragility can be defined as “the quality of being easily broken or damaged” Porter (A Beginner’s guide to fragility, vulnerability, and risk. Springer, Berlin, 2015).
