Mathematical definition, mapping, and detection of (anti)fragility

@article{Taleb2012MathematicalDM,
  title={Mathematical definition, mapping, and detection of (anti)fragility},
  author={Nassim Nicholas Taleb and Raphael Douady},
  journal={Quantitative Finance},
  year={2012},
  volume={13},
  pages={1677 - 1689}
}
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… 

Radical Uncertainty, Non-Predictability, Antifragility and Risk-Sharing Islamic Finance

Under conditions of radical uncertainty, risk sharing renders financial systems anti-fragile. Our goal in this paper is to show that risk-sharing Islamic finance (RSIF) shares the characteristics

Measuring Banks’ Antifragility via Fuzzy Logic

TLDR
The creation of the Banking Antifragility Index (BAI) is proposed, which is based on the calculation of a triangular fuzzy number – to "quantify" qualitative criteria linked to ant ifragility.

Managing the Downside of Active and Passive Strategies: Convexity and Fragilities

  • R. Douady
  • Economics
    SSRN Electronic Journal
  • 2019
Question of the day: how to manage a large (or small) portfolio in low interest rate conditions, while equity markets bear significant draw-down risk? More generally, how to build an “antifragile”

Stocks and Cryptocurrencies: Anti-fragile or Robust?

Antifragility was recently defined as a property of complex systems that benefit from disorder. However, its original formal definition is difficult to apply. Our approach has been to define and test

Managing the Downside of Active and Passive Strategies—Part 1: Convexity and Fragilities

  • R. Douady
  • Economics
    The Journal of Portfolio Management
  • 2019
In this article, the author addresses the question of how to manage a large (or small) portfolio in low interest rate conditions while equity markets bear significant drawdown risk. More generally,

Stocks and Cryptocurrencies: Antifragile or Robust? A Novel Antifragility Measure of the Stock and Cryptocurrency Markets

In contrast with robust systems that resist noise or fragile systems that break with noise, antifragility is defined as a property of complex systems that benefit from noise or disorder. Here we

Anti)Fragility and Convex Responses in Medicine

TLDR
A framework to integrate the necessary consequences of nonlinearities in evidence-based medicine and medical risk management is proposed, linking probability to nonlinearity of response.

On the statistical differences between binary forecasts and real-world payoffs

  • N. Taleb
  • Economics
    International Journal of Forecasting
  • 2020

Anti-Fragile Information Systems Completed Research

TLDR
A set of guidelines for moving from the fragile toward the antifragile is proposed, and for the processes of the IS function, their applications and the questions they raise for practice and research are explored.
...

References

SHOWING 1-10 OF 26 REFERENCES

A New Heuristic Measure of Fragility and Tail Risks: Application to Stress Testing

This paper presents a simple heuristic measure of tail risk, which is applied to individual bank stress tests and to public debt. Stress testing can be seen as a first order test of the level of

Errors, Robustness, and the Fourth Quadrant

Antifragile: Things That Gain from Disorder

ANTIFRAGILE: THINGS THAT GAIN FROM DISORDER Nassim Nicholas Taleb Random House, New York, 2012, 519 pp. ISBN: 978-1-4000-6782-4Antifragile is a book about the structure and behavior of dynamic

ON THE THEORY OF RISK AVERSION

the existing theory by establishing the economic significance of the partial relative risk aversion function. Let u(t) be a utility function for wealth. The functions A(t) = -u"(t)/u'(t) and R(t)

Risk Aversion in the Small and in the Large. When Outcomes are Multidimensional

The paper discusses criteria for comparing risk aversion of decision makers when outcomes are multidimensional. A weak concept, "commodity specific greater risk aversion", is based on the comparison

Prospect theory: analysis of decision under risk

Analysis of decision making under risk has been dominated by expected utility theory, which generally accounts for people's actions. Presents a critique of expected utility theory as a descriptive

Homo Heuristicus: Why Biased Minds Make Better Inferences

TLDR
The study of heuristics shows that less information, computation, and time can in fact improve accuracy, in contrast to the widely held view that less processing reduces accuracy.

Dynamic Hedging: Managing Vanilla and Exotic Options

Partial table of contents: MARKETS, INSTRUMENTS, PEOPLE. The Generalized Option. Liquidity and Liquidity Holes. Volatility and Correlation. MEASURING OPTION RISKS. Gamma and Shadow Gamma. Theta and

Reasoning the fast and frugal way: models of bounded rationality.

TLDR
The authors have proposed a family of algorithms based on a simple psychological mechanism: one-reason decision making, and found that these fast and frugal algorithms violate fundamental tenets of classical rationality: they neither look up nor integrate all information.