Comment on "Are financial crashes predictable?"

Comment on "Are financial crashes predictable?", L. Laloux, M. Potters, R. Cont, J.P Aguilar and J.-P. Bouchaud, Europhys. Lett. 45, 1-5 (1999)Comment: 2 pages including 2 figures. Subm. to Eur. Phys Lett. Previous error in fig. 1 correcte

Bouchaud-M\'ezard model on a random network

We studied the Bouchaud-M\'ezard(BM) model, which was introduced to explain Pareto's law in a real economy, on a random network. Using "adiabatic and independent" assumptions, we analytically obtained the stationary probability distribution function of wealth. The results shows that wealth-condensation, indicated by the divergence of the variance of wealth, occurs at a larger $J$ than that obtained by the mean-field theory, where $J$ represents the strength of interaction between agents. We compared our results with numerical simulation results and found that they were in good agreement.Comment: to be published in Physical Review

Breakdown of the mean-field approximation in a wealth distribution model

One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and M\'ezard have proposed an interesting model of economy [Bouchaud and M\'ezard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.Comment: 11 pages, 3 figure

Cont-Bouchaud percolation model including Tobin tax

The Tobin tax is an often discussed method to tame speculation and get a source of income. The discussion is especially heated when the financial markets are in crisis. In this article we refer to foreign exchange markets. The Tobin tax should be a small international tax affecting all currency transactions and thus consequently reducing the destabilizing speculations. In this way this tax should take over a control function. By including Tobin tax in the microscopic model of Cont and Bouchaud one finds that Tobin tax could be the right method to control foreign exchange operations and get a good source of incomeComment: Expanded for of paper to be published in Int. J. Mod. Phys. C 13 (2002

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter \Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperature-like parameter \eta(\Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favourably with a range of known experimental behaviour. This includes the logarithmic densification and power spectrum of fluctuations under constant \eta, the annealing curve when \eta is varied cyclically in time, and memory effects observed for a discontinuous shift in \eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.Comment: 2 references added; some figure labels tweaked. To appear in PR

Hierarchical Cont-Bouchaud model

We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdos-Renyi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdos-Renyi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.Comment: 10 pages, 6 figure