Stochastic Lotka-Volterra Systems of Competing Auto-Catalytic Agents Lead Generically to Truncated Pareto Power Wealth Distribution, Truncated Levy Distribution of Market Returns, Clustered Volatility, Booms and Craches

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).Comment: 13 Pages, no figure

Microeconomic Structure determines Macroeconomic Dynamics. Aoki defeats the Representative Agent

Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fractal / intermittent fluctuations of macroeconomic quantities from the granularity of the mezo-economic collective objects (large individual wealth, highly productive geographical locations, emergent technologies, emergent economic sectors) in which the micro-economic agents self-organize. In particular, we present some theoretical predictions, which also met extensive validation from empirical data in a wide range of systems: - The fractal Levy exponent of the stock market index fluctuations equals the Pareto exponent of the investors wealth distribution. The origin of the macroeconomic dynamics is therefore found in the granularity induced by the wealth / capital of the wealthiest investors. - Economic cycles consist of a Schumpeter 'creative destruction' pattern whereby the maxima are cusp-shaped while the minima are smooth. In between the cusps, the cycle consists of the sum of 2 'crossing exponentials': one decaying and the other increasing. This unification within the same theoretical framework of short term market fluctuations and long term economic cycles offers the perspective of a genuine conceptual synthesis between micro- and macroeconomics. Joining another giant of contemporary science - Phil Anderson - Aoki emphasized the role of rare, large fluctuations in the emergence of macroeconomic phenomena out of microscopic interactions and in particular their non self-averaging, in the language of statistical physics. In this light, we present a simple stochastic multi-sector growth model.Comment: 42 pages, 6 figure

Uncovering the dynamics of citations of scientific papers

We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has far-reaching consequences, such as diverging citation distributions and runaway papers. We propose a nonlinear stochastic dynamic model of citation dynamics based on link copying/redirection mechanism. The model is fully calibrated by empirical data and does not contain free parameters. This model can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.Comment: 18 pages, 7 figure