This review presents a general theory of financial crashes and of stock market instabilities that his co-workers and the author have developed over the past seven years. We start by discussing the limitation of standard analyses for characterizing how crashes are special. The study of the frequency distribution of drawdowns, or runs of successive losses shows that large financial crashes are "outliers": they form a class of their own as can be seen from their statistical signatures. If large financial crashes are "outliers", they are special and thus require a special explanation, a specific model, a theory of their own. In addition, their special properties may perhaps be used for their prediction. The main mechanisms leading to positive feedbacks, i.e., self-reinforcement, such as imitative behavior and herding between investors are reviewed with many references provided to the relevant literature outside the narrow confine of Physics. Positive feedbacks provide the fuel for the development of speculative bubbles, preparing the instability for a major crash. We demonstrate several detailed mathematical models of speculative bubbles and crashes. A first model posits that the crash hazard drives the market price. The crash hazard may sky-rocket at some times due to the collective behavior of "noise traders", those who act on little information, even if they think they "know". A second-version inverses the logic and posits that prices drive the crash hazard. Prices may skyrocket at some times again due to the speculative or imitative behavior of investors. According the rational expectation model, this entails automatically a corresponding increase of the probability for a crash. We also review two other models including the competition between imitation and contrarian behavior and between value investors and technical analysts. The most important message is the discovery of robust and universal signatures of the approach to crashes. These precursory patterns have been documented for essentially all crashes on developed as well as emergent stock markets, on currency markets, on company stocks, and so on. We review this discovery at length and demonstrate how to use this insight and the detailed predictions obtained from these models to forecast crashes. For this, we review the major crashes of the past that occurred on the major stock markets of the planet and describe the empirical evidence of the universal nature of the critical log-periodic precursory signature of crashes. The concept of an "anti-bubble" is also summarized, with the Japanese collapse from the beginning of 1991 to present, taken as a prominent example. A prediction issued and advertised in January 1999 has been until recently born out with remarkable precision, predicting correctly several changes of trends, a feat notoriously difficult using standard techniques of economic forecasting. We also summarize a very recent analysis the behavior of the U.S. S&P500 index from 1996 to August 2002 and the forecast for the two following years. We conclude by presenting our view of the organization of financial markets. (C) 2003 Elsevier Science B.V. All rights reserved.
