1998/03/30 by Sorin Solomon, Solomon, Sorin
Decision Sciences · Economics, Econometrics and Finance · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #Computational Physics (physics.comp-ph) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Economics and business #FOS: Physical sciences #General Finance (q-fin.GN) #Innovation Diffusion and Forecasting #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.cond-mat/9803367
openalex publication_date 1998/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a microscopic representation of the stock-market in which the microscopic agents are the individual traders and their capital. Their basic dynamics consists in the auto-catalysis of the individual capital and in the global competition/cooperation between the agents mediated by the total wealth invested in the stock (which we identify with the stock-index). We show that such systems lead generically to (truncated) Pareto power-law distribution of the individual wealth. This, in turn, leads to intermittent market (short time) returns parametrized by a (truncated) Levy distribution. We relate the truncation in the Levy distribution to the (truncation in the Pareto Power Law i.e. to the) fact that at each moment no trader can own more than the current total wealth invested in the stock. In the cases where the system is dominated by the largest traders, the dynamics looks similar to noisy low-dimensional chaos. By introducing traders memory and/or feedback between individual and collective wealth fluctuations (the later identified with the stock returns), one obtains clustered "volatility" as well as market booms and crashes. The basic feedback loop consists in: - computing the market price of the stock as the sum of the individual wealths invested in the stock by the traders and - determining the time variation of the individual trader wealth as his/her previous wealth multiplied by the stock return (i.e. the variation of the stock price).