47 research outputs found
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
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
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
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.
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
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
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
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
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