Sornette’s … Prediction of Crises

Sornette, D  Dragon-Kings, Black Swans and the Prediction of Crises 2009


The presence of a phase transition [aka a catastrophe … or a tipping point] is crucial to learn how to diagnose in advance the symptoms associated with a coming [crisis].

1. Introduction

Systems with a large number of mutually interacting parts, often open to their environment, self-organize their internal structure and their dynamics with novel and sometimes surprising macroscopic (“emergent”) properties.

we introduce the concept of dragon-kings to refer to the existence of transient organization into extreme events that are statistically and mechanistically different from the rest of their smaller siblings. This realization opens the way for a systematic theory of predictability of catastrophes … .

2. Power law distributions …

Many interesting examples of data that fit power-law models are given.

Power law distributions incarnate the notion that extreme events are not exceptional events. Instead, extreme events should be considered to be rather frequent and to result from the same organization principle(s) as those generating other events: because they belong to the same statistical distribution, this suggests common generating mechanism(s).

3. Beyond power laws: dragon-king outliers

Dragon Kings are significant outliers to the supposed power-laws, more common than they ‘should’ be. They also appear not to be incidental or accidental. Examples are given, typically involving coupling between sub-systems that otherwise vary dynamically.

4. Consequences of the dragon-king phenomenon …

I have presented a preliminary review of the methods based on these insights to predict material rupture, turbulence bursts, abrupt changes in weather regimes, financial crashes and human birth.

The key idea is that catastrophic events involve interactions between structures at many different scales that lead to the emergence of transitions between collective regimes of organization.

These qualitative changes … take engineers, practitioners and students by surprise, because of the ubiquitous tendency to extrapolate new behavior from past ones.

The main concepts that are needed to understand stock markets are imitation, herding, self-organized cooperativity and positive feedbacks, leading to the development of endogenous instabilities. [L]ocal effects such as interest raises, new tax laws, new regulations and so on … are only one of the triggering factors but not the fundamental cause of the bubble collapse.

Mathematically, large stock market crashes are the social analogues of so-called critical points studied in the statistical physics community in relation to magnetism, melting, and other phase transformation of solids, liquids, gas and other phases of matter. This theory is based on the existence of a cooperative behavior of traders imitating each other which leads to progressively increasing build-up of market cooperativity, or effective interactions between investors, often translated into accelerating ascent of the market price over months and years before the crash.

It is important to stress that our methodology allows us to predict the end of bubbles, but not the crashes per se. … The end of a bubble may be a plateau or a slow decay.

See also

Smuts for a generalization and Whitehead* and Keynes* for the underlying theory.


  • Sornette contradicts the supposition that there is a common statistical distribution (e.g. a ‘power law’) than underlies crises, but does not consider whether ‘Dragon Kings’ belong to any distribution. That is, could we consider Dragon Kings to be random samples from some given space of possibilities, according to some (complicated) distribution, or are they sometimes more ‘creative’? Is it enough (as Sornette proposes) to look at outcome data, or (as Keynes suggests) might we need  to look deeper. For example, from 2005 on which was more informative, stock price indexes or talking to friends discussing ‘buy to let’?
  • Sornette is critical of cooperativity in the market. But were people being irrational? In QDT Sornette describes human decision making as taking account, irrationally, of uncertainty. But standard decision theory relies on utilities which assume – in effect – that situations are statistical. But if Dragon Kings are truly surprising and hence lack given statistical properties then there is no basis for conventional decision-making: human decision making, with its preference for avoiding Dragon Kings, may be preferable.
  • Sornette’s picture is similar to that in Turing’s Morphogenesis, which has a useful classification of what may happen when a ‘bubble’ ends. In particular, one may have oscillatory behaviour, not just plateaus, slow decays or crashes.

 Dave Marsay

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