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Dragon-Kings, Black Swans and the Prediction of Crises


Didier Sornette


Swiss Finance Institute; ETH Zurich

September 8, 2009

Swiss Finance Institute Research Paper No. 09-36

Abstract:     
We develop the concept of “dragon-kings” corresponding to meaningful outliers, which are found to coexist with power laws in the distributions of event sizes under a broad range of conditions in a large variety of systems. These dragon-kings reveal the existence of mechanisms of self-organization that are not apparent otherwise from the distribution of their smaller siblings. We present a generic phase diagram to explain the generation of dragon-kings and document their presence in six different examples (distribution of city sizes, distribution of acoustic emissions associated with material failure, distribution of velocity increments in hydrodynamic turbulence, distribution of financial drawdowns, distribution of the energies of epileptic seizures in humans and in model animals, distribution of the earthquake energies). We emphasize the importance of understanding dragon-kings as being often associated with a neighborhood of what can be called equivalently a phase transition, a bifurcation, a catastrophe (in the sense of René Thom), or a tipping point. The presence of a phase transition is crucial to learn how to diagnose in advance the symptoms associated with a coming dragon-king. Several examples of predictions using the derived log-periodic power law method are discussed, including material failure predictions and the forecasts of the end of financial bubbles.

Number of Pages in PDF File: 21

Keywords: outliers,; kings, red dragons, extremes, crisis, catastrophes, bifurcations, power laws, prediction

JEL Classification: C50, G01, G17

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Date posted: September 8, 2009  

Suggested Citation

Sornette, Didier, Dragon-Kings, Black Swans and the Prediction of Crises (September 8, 2009). Swiss Finance Institute Research Paper No. 09-36. Available at SSRN: http://ssrn.com/abstract=1470006 or http://dx.doi.org/10.2139/ssrn.1470006

Contact Information

Didier Sornette (Contact Author)
Swiss Finance Institute ( email )
c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland
ETH Zurich ( email )
Department of Management, Technology and Economics
Scheuchzerstrasse 7
8092 Zurich
Switzerland
41446328917 (Phone)
41446321914 (Fax)
HOME PAGE: http://www.er.ethz.ch/
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