Critical Market Crashes

This review is a partial synthesis of the book ``Why stock market crash'' (Princeton University Press, January 2003), which 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. 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 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. 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. The concept of an ``anti-bubble'' is also summarized, with two forward predictions on the Japanese stock market starting in 1999 and on the USA stock market still running. We conclude by presenting our view of the organization of financial markets.Comment: Latex 89 pages and 38 figures, in press in Physics Report

Random Walk Access Times on Partially-Disordered Complex Networks: an Effective Medium Theory

An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are different for steps across lattice bonds from the rates $f$ across network shortcuts. The theory is developed for structures with arbitrary shortcut distributions and applied to a class of partially-disordered traversal enhanced networks in which shortcuts of fixed length are distributed randomly with finite probability. Numerical simulations are found to be in excellent agreement with predictions of the effective medium theory on all aspects addressed by the latter. Access times for random walks on these partially disordered structures are compared to those on small-world networks, which on average appear to provide the most effective means of decreasing access times uniformly across the network.Comment: 12 pages, 8 figures; added new results and discussion; added appendix on numerical procedures. To appear in PR