Farming and husbandry of black swans and dragon kings

Heavy tailed and Knightian uncertainties for fun and profit

There are several things that people seem to conflate when talking about black swans: heavy tails and unknown unknowns, nonstationarity… Nassim Taleb has indeed talked about all of these concepts; He does not refer to them all as swans tho’ AFAIK.

What I think of in this context is portfolio theory for a world of outliers.

I have nothing new to add yet, so I’ll just punt you to my bookmarked favoured essays on this theme.

Rohit, Spot The Outlier is exemplary:

In a world of plenty, selection is hard. In a world where selection is hard, we resort to ever more stringent measurement. But if measurement is too strict, we lose out on variance. If we lose out on variance, we miss out on what actually impacts outcomes. If we miss what actually impacts outcomes, we think we’re in a rut. But we might not be! Once you’ve weeded out the clear “no” s, then it’s better to bet on variance rather than trying to ascertain the true mean through imprecise means.

Black swans

Dragon kings

Some distributions are so heavy tailed that we should expect that one event from that is bigger than all the others put together. These are called Dragon Kings (Sornette 2009). It has been argued, for example, that nuclear disasters are likely of this type (Wheatley, Sovacool, and Sornette 2017). TBC

Knightian uncertainty

Important terminology for unknown unknowns.

Countercyclical philanthropy

If a charity is dedicated to dealing with unpredictable events, what does this say about the financial structures they should employ? MSF’s activity in war zones, for example. TBC


Cirillo, Pasquale, and Nassim Nicholas Taleb. 2020. Tail Risk of Contagious Diseases.” Nature Physics 16 (6): 606–13.
Lux, Thomas, and Didier Sornette. 2002. On Rational Bubbles and Fat Tails.” Journal of Money, Credit and Banking 34: 589–610.
Shen, Chen, Nassim Nicholas Taleb, and Yaneer Bar-Yam. 2020. Review of Ferguson Et Al ‘Impact of Non-Pharmaceutical Interventions…’.” New England Complex Systems Institute.
Sornette, Didier. 2003. Critical Market Crashes.” Physics Reports 378 (1): 1–98.
———. 2009. Dragon-Kings, Black Swans and the Prediction of Crises.” arXiv:0907.4290 [Physics] 2 (1).
Sornette, Didier, and Peter Cauwels. 2015. Managing Risk in a Creepy World.” Journal of Risk Management in Financial Institutions 8 (1): 83–108.
Taleb, Nassim Nicholas. 2007. Black Swans and the Domains of Statistics.” The American Statistician 61 (3): 198–200.
———. 2010. The Black Swan:The Impact of the Highly Improbable: With a new section: “On Robustness and Fragility”. 2nd ed. edition. New York: Random House Publishing Group.
———. 2013. Where Do Thin Tails Come From? arXiv:1307.6695 [Physics, q-Fin, Stat], July.
———. 2018. Election Predictions as Martingales: An Arbitrage Approach.” Quantitative Finance 18 (1): 1–5.
———. 2020. On the Statistical Differences Between Binary Forecasts and Real-World Payoffs.” International Journal of Forecasting, April.
Weitzman, Martin L. 2011. Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change.” Review of Environmental Economics and Policy 5 (2): 275–92.
Wheatley, Spencer, Benjamin Sovacool, and Didier Sornette. 2017. Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents and Accidents.” Risk Analysis 37 (1): 99–115.

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