Mathematical Definition of Anti-Fragility Mathematical Definition, Mapping, and Detection of (Anti)Fragility
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.
https://arxiv.org/pdf/1208.1189.pdf
optionality
Taleb's 2007 book, "Black Swan: The Nature of Uncertainty and Risk," sold 1.5 million copies in the United States after the Lehman Brothers collapse, which was triggered by the subprime mortgage meltdown. Taleb says anti-fragility means having options. Options are what make us anti-fragile. With options, we can benefit from the positive side of uncertainty without being seriously harmed by the negative side of uncertainty.
What does it take for a maker to become "anti-fragile"? : Let's go with design thinking!
Making Uncertainty Your Ally in "Anti-Fragility" | Sigotano!
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