Avik’s Ruminations

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Black Swans and Dragon Kings

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A new paper by Didier Sornette at ETF Zurich adds  the concepts of Dragon Kings  to our understanding of rare large events. While a black swan event is seen as being generated by the the same statistical power law distribution that generates small events, the author considers dragon king events as that exist beyond the normal power law distribution. However he suggests that the lower heterogeneity can lead to better predictability, even if it also leads to a more catastrophic outcome.

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 Rene 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.

Written by Avik Sengupta

July 27th, 2009 at 11:01 pm

Posted in Finance

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