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

Author

Listed:
  • Nassim Nicholas Taleb

    (NYU Polytechnic School of Engineering)

  • Raphaël Douady

    (Riskdata - Financial Risk Management Software, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

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 improves on stress testing and bypasses the cillib flaws in Value-at-Risk.

Suggested Citation

  • Nassim Nicholas Taleb & Raphaël Douady, 2014. "Mathematical Definition, Mapping, and Detection of (Anti)Fragility," Post-Print hal-01151340, HAL.
  • Handle: RePEc:hal:journl:hal-01151340
    Note: View the original document on HAL open archive server: https://hal.science/hal-01151340
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    References listed on IDEAS

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    1. Taleb, Nassim Nicholas, 2009. "Errors, robustness, and the fourth quadrant," International Journal of Forecasting, Elsevier, vol. 25(4), pages 744-759, October.
    2. Mr. Christian Schmieder & Mr. Tidiane Kinda & Mr. Nassim N. Taleb & Ms. Elena Loukoianova & Mr. Elie Canetti, 2012. "A New Heuristic Measure of Fragility and Tail Risks: Application to Stress Testing," IMF Working Papers 2012/216, International Monetary Fund.
    3. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    4. Haug, Espen Gaarder & Taleb, Nassim Nicholas, 2011. "Option traders use (very) sophisticated heuristics, never the Black-Scholes-Merton formula," Journal of Economic Behavior & Organization, Elsevier, vol. 77(2), pages 97-106, February.
    5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    6. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
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    Cited by:

    1. Nassim N. Taleb, 2012. "How We Tend To Overestimate Powerlaw Tail Exponents," Papers 1210.1966, arXiv.org.
    2. Tran, Huy T. & Balchanos, Michael & Domerçant, Jean Charles & Mavris, Dimitri N., 2017. "A framework for the quantitative assessment of performance-based system resilience," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 73-84.
    3. Bellè, Andrea & Zeng, Zhiguo & Duval, Carole & Sango, Marc & Barros, Anne, 2022. "Modeling and vulnerability analysis of interdependent railway and power networks: Application to British test systems," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    4. Samiul Hasan & Greg Foliente, 2015. "Modeling infrastructure system interdependencies and socioeconomic impacts of failure in extreme events: emerging R&D challenges," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 78(3), pages 2143-2168, September.
    5. Taleb, Nassim Nicholas, 2020. "On the statistical differences between binary forecasts and real-world payoffs," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1228-1240.
    6. Dar'io Alatorre & Carlos Gershenson & Jos'e L. Mateos, 2020. "Stocks and Cryptocurrencies: Anti-fragile or Robust?," Papers 2005.13033, arXiv.org, revised Jul 2022.
    7. Ahmadreza Ghasemi & Mitra Alizadeh, 2017. "Evaluating organizational antifragility via fuzzy logic. The case of an Iranian company producing banknotes and security paper," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(2), pages 21-43.
    8. Nassim Nicholas Taleb & Rupert Read & Raphaël Douady & Joseph Norman & Yaneer Bar-Yam, 2014. "The Precautionary Principle (with Application to the Genetic Modification of Organisms)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01479405, HAL.
    9. Tan, Raymond R. & Aviso, Kathleen B. & Chiu, Anthony S.F. & Promentilla, Michael Angelo B. & Razon, Luis F. & Tseng, Ming-Lang & Yu, Krista Danielle S., 2017. "Towards “climate-proof” industrial networks," Resources, Conservation & Recycling, Elsevier, vol. 127(C), pages 244-245.
    10. Mahata, Ajit & Rai, Anish & Nurujjaman, Md. & Prakash, Om, 2021. "Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shape recovery," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    11. Lalisa A. Duguma & Meine van Noordwijk & Peter A. Minang & Kennedy Muthee, 2021. "COVID-19 Pandemic and Agroecosystem Resilience: Early Insights for Building Better Futures," Sustainability, MDPI, vol. 13(3), pages 1-22, January.
    12. Meine van Noordwijk & Erika Speelman & Gert Jan Hofstede & Ai Farida & Ali Yansyah Abdurrahim & Andrew Miccolis & Arief Lukman Hakim & Charles Nduhiu Wamucii & Elisabeth Lagneaux & Federico Andreotti , 2020. "Sustainable Agroforestry Landscape Management: Changing the Game," Land, MDPI, vol. 9(8), pages 1-38, July.
    13. Yuri Biondi & Pierpaolo Giannoccolo, 2015. "Share price formation, market exuberance and financial stability under alternative accounting regimes," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(2), pages 333-362, October.
    14. Raphaël Douady, 2019. "Managing the Downside of Active and Passive Strategies: Convexity and Fragilities," Post-Print hal-02488589, HAL.
    15. Apanisile Temitope Samuel, 2024. "The Justification of Complex Systems Analysis in Better Informing Project Decisions: A Study of the us Surface Transportation Board," International Journal of Research and Scientific Innovation, International Journal of Research and Scientific Innovation (IJRSI), vol. 11(8), pages 263-280, August.
    16. Kourtit, Karima & Nijkamp, Peter & Banica, Alexandru, 2023. "An analysis of natural disasters’ effects – A global comparative study of ‘Blessing in Disguise’," Socio-Economic Planning Sciences, Elsevier, vol. 88(C).
    17. Evangelos Gkanatsas & Harold Krikke, 2020. "Towards a Pro-Silience Framework: A Literature Review on Quantitative Modelling of Resilient 3PL Supply Chain Network Designs," Sustainability, MDPI, vol. 12(10), pages 1-25, May.
    18. Harald de Bruijn & Andreas Größler & Nuno Videira, 2020. "Antifragility as a design criterion for modelling dynamic systems," Systems Research and Behavioral Science, Wiley Blackwell, vol. 37(1), pages 23-37, January.
    19. Atif Ansar & Bent Flyvbjerg & Alexander Budzier & Daniel Lunn, 2016. "Big is Fragile: An Attempt at Theorizing Scale," Papers 1603.01416, arXiv.org, revised Jun 2017.
    20. Giuseppe Montesi & Giovanni Papiro, 2018. "Bank Stress Testing: A Stochastic Simulation Framework to Assess Banks’ Financial Fragility †," Risks, MDPI, vol. 6(3), pages 1-54, August.
    21. Kalantari, Somayeh & Nazemi, Eslam & Masoumi, Behrooz, 2021. "Entropy-based goal-oriented emergence management in self-organizing systems through feedback control loop: A case study in NASA ANTS mission," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

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    More about this item

    Keywords

    impulse response; Jensen inequality; stress testing; fragility;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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