Power-Law Distributions in Circulating Money: Effect of Preferential Behavior

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mechanism to ensure the robustness of power-law distributions.Comment: 4 pages, 2 figure

Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact

We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. The slope of the exponential function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the exponential law continuously evolves into Gaussian distribution. The exponential-to-Gaussian crossover is well described by the analytical solution of the Heston model with stochastic volatility.Comment: 7 pages, 12 plots, elsart.cls, submitted to the Proceedings of APFA-4. V.2: updated reference

Kinetic Exchange Models for Income and Wealth Distributions

Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium. However, it also deviates in the low income and more significantly for the high income ranges. Application of physics models provides illuminating ideas and understanding, complementing the observations.Comment: 15 pages, 20 eps figures, EPJ class; To be published as "Colloquium" in Eur Phys J

Inelastically scattering particles and wealth distribution in an open economy

Using the analogy with inelastic granular gasses we introduce a model for wealth exchange in society. The dynamics is governed by a kinetic equation, which allows for self-similar solutions. The scaling function has a power-law tail, the exponent being given by a transcendental equation. In the limit of continuous trading, closed form of the wealth distribution is calculated analytically.Comment: 8 pages 5 figure

Kinetic market models with single commodity having price fluctuations

We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: Gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.Comment: RevTeX4, 6 pages, 5 eps figures, accepted in Eur. Phys. J.

Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Dt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval Dt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.Comment: 5 pages, 7 figures, RevTeX, proceedings of APFA-5. V.2: minor typos corrected, 2 references adde

Dynamics of Transformation from Segregation to Mixed Wealth Cities

We model the dynamics of the Schelling model for agents described simply by a continuously distributed variable - wealth. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the threshold level. As in the case of the classic Schelling model where segregation obtains between two races, we find here that wealth-based segregation occurs and persists. However, introducing uncertainty into the decision to move - that is, with some probability, if agents are allowed to move even though the threshold level condition is contravened - we find that even for small proportions of such disallowed moves, the dynamics no longer yield segregation but instead sharply transition into a persistent mixed wealth distribution. We investigate the nature of this sharp transformation between segregated and mixed states, and find that it is because of a non-linear relationship between allowed moves and disallowed moves. For small increases in disallowed moves, there is a rapid corresponding increase in allowed moves, but this tapers off as the fraction of disallowed moves increase further and finally settles at a stable value, remaining invariant to any further increase in disallowed moves. It is the overall effect of the dynamics in the initial region (with small numbers of disallowed moves) that shifts the system away from a state of segregation rapidly to a mixed wealth state. The contravention of the tolerance condition could be interpreted as public policy interventions like minimal levels of social housing or housing benefit transfers to poorer households. Our finding therefore suggests that it might require only very limited levels of such public intervention - just sufficient to enable a small fraction of disallowed moves, because the dynamics generated by such moves could spur the transformation from a segregated to mixed equilibrium.Comment: 12 pages, 7 figure

Self-similarity and power-like tails in nonconservative kinetic models

In this paper, we discuss the large--time behavior of solution of a simple kinetic model of Boltzmann--Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the nonlinearity and of the time--monotonicity of the temperature, the kinetic model has non trivial quasi-stationary states with power law tails. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution. The same idea is applied to investigate the large-time behavior of an elementary kinetic model of economy involving both exchanges between agents and increasing and/or decreasing of the mean wealth. In this last case, the large-time behavior of the solution shows a Pareto power law tail. Numerical results confirm the previous analysis

Is the Equivalence Principle violated by Generalized Uncertainty Principles and Holography in a brane-world?

It has been recently debated whether a class of generalized uncertainty principles that include gravitational sources of error are compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space-time dimensions are present. However, we shall show here that the validity of the holographic counting can be maintained also in models with extra spatial dimensions, but at the intriguing price that the equivalence principle for a point-like source be violated and the inertial mass differ from the gravitational mass in a specific non-trivial way.Comment: 5 pages, latex fil

Exploiting the flexibility of a family of models for taxation and redistribution

We discuss a family of models expressed by nonlinear differential equation systems describing closed market societies in the presence of taxation and redistribution. We focus in particular on three example models obtained in correspondence to different parameter choices. We analyse the influence of the various choices on the long time shape of the income distribution. Several simulations suggest that behavioral heterogeneity among the individuals plays a definite role in the formation of fat tails of the asymptotic stationary distributions. This is in agreement with results found with different approaches and techniques. We also show that an excellent fit for the computational outputs of our models is provided by the k-generalized distribution introduced by G. Kaniadakis (Physica A 296 (2001) 405-425).Comment: 17 pages, 5 figures. Accepted for publication in Eur. Phys. J. B. arXiv admin note: text overlap with arXiv:1109.060