36 research outputs found
Wealth distribution in an ancient Egyptian society
Modern excavations yielded a distribution of the house areas in the ancient
Egyptian city Akhetaten, which was populated for a short period during the 14th
century BC. Assuming that the house area is a measure of the wealth of its
inhabitants allows us to make a comparison of the wealth distributions in
ancient and modern societies
Long-Time Fluctuations in a Dynamical Model of Stock Market Indices
Financial time series typically exhibit strong fluctuations that cannot be
described by a Gaussian distribution. In recent empirical studies of stock
market indices it was examined whether the distribution P(r) of returns r(tau)
after some time tau can be described by a (truncated) Levy-stable distribution
L_{alpha}(r) with some index 0 < alpha <= 2. While the Levy distribution cannot
be expressed in a closed form, one can identify its parameters by testing the
dependence of the central peak height on tau as well as the power-law decay of
the tails. In an earlier study [Mantegna and Stanley, Nature 376, 46 (1995)] it
was found that the behavior of the central peak of P(r) for the Standard & Poor
500 index is consistent with the Levy distribution with alpha=1.4. In a more
recent study [Gopikrishnan et al., Phys. Rev. E 60, 5305 (1999)] it was found
that the tails of P(r) exhibit a power-law decay with an exponent alpha ~= 3,
thus deviating from the Levy distribution. In this paper we study the
distribution of returns in a generic model that describes the dynamics of stock
market indices. For the distributions P(r) generated by this model, we observe
that the scaling of the central peak is consistent with a Levy distribution
while the tails exhibit a power-law distribution with an exponent alpha > 2,
namely beyond the range of Levy-stable distributions. Our results are in
agreement with both empirical studies and reconcile the apparent disagreement
between their results
The origin of power-law distributions in self-organized criticality
The origin of power-law distributions in self-organized criticality is
investigated by treating the variation of the number of active sites in the
system as a stochastic process. An avalanche is then regarded as a first-return
random walk process in a one-dimensional lattice. Power law distributions of
the lifetime and spatial size are found when the random walk is unbiased with
equal probability to move in opposite directions. This shows that power-law
distributions in self-organized criticality may be caused by the balance of
competitive interactions. At the mean time, the mean spatial size for
avalanches with the same lifetime is found to increase in a power law with the
lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in
J. Phys.
On a kinetic model for a simple market economy
In this paper, we consider a simple kinetic model of economy involving both
exchanges between agents and speculative trading. We show that the kinetic
model admits non trivial quasi-stationary states with power law tails of Pareto
type. In order to do this we consider a suitable asymptotic limit of the model
yielding a Fokker-Planck equation for the distribution of wealth among
individuals. For this equation the stationary state can be easily derived and
shows a Pareto power law tail. Numerical results confirm the previous analysis
Volatility Effects on the Escape Time in Financial Market Models
We shortly review the statistical properties of the escape times, or hitting
times, for stock price returns by using different models which describe the
stock market evolution. We compare the probability function (PF) of these
escape times with that obtained from real market data. Afterwards we analyze in
detail the effect both of noise and different initial conditions on the escape
time in a market model with stochastic volatility and a cubic nonlinearity. For
this model we compare the PF of the stock price returns, the PF of the
volatility and the return correlation with the same statistical characteristics
obtained from real market data.Comment: 12 pages, 9 figures, to appear in Int. J. of Bifurcation and Chaos,
200
Mesoscopic modelling of financial markets
We derive a mesoscopic description of the behavior of a simple financial
market where the agents can create their own portfolio between two investment
alternatives: a stock and a bond. The model is derived starting from the
Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using
the methods of kinetic theory and consists of a linear Boltzmann equation for
the wealth distribution of the agents coupled with an equation for the price of
the stock. From this model, under a suitable scaling, we derive a Fokker-Planck
equation and show that the equation admits a self-similar lognormal behavior.
Several numerical examples are also reported to validate our analysis
Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements
A generic model of stochastic autocatalytic dynamics with many degrees of
freedom is studied using computer simulations. The time
evolution of the 's combines a random multiplicative dynamics at the individual level with a global coupling through a
constraint which does not allow the 's to fall below a lower cutoff given
by , where is their momentary average and is a
constant. The dynamic variables are found to exhibit a power-law
distribution of the form . The exponent
is quite insensitive to the distribution of the random factor
, but it is non-universal, and increases monotonically as a function
of . The "thermodynamic" limit, N goes to infty and the limit of decoupled
free multiplicative random walks c goes to 0, do not commute:
for any finite while (which is the common range
in empirical systems) for any positive . The time evolution of exhibits intermittent fluctuations parametrized by a (truncated)
L\'evy-stable distribution with the same index . This
non-trivial relation between the distribution of the 's at a given time
and the temporal fluctuations of their average is examined and its relevance to
empirical systems is discussed.Comment: 7 pages, 4 figure
Runaway Events Dominate the Heavy Tail of Citation Distributions
Statistical distributions with heavy tails are ubiquitous in natural and
social phenomena. Since the entries in heavy tail have disproportional
significance, the knowledge of its exact shape is very important. Citations of
scientific papers form one of the best-known heavy tail distributions. Even in
this case there is a considerable debate whether citation distribution follows
the log-normal or power-law fit. The goal of our study is to solve this debate
by measuring citation distribution for a very large and homogeneous data. We
measured citation distribution for 418,438 Physics papers published in
1980-1989 and cited by 2008. While the log-normal fit deviates too strong from
the data, the discrete power-law function with the exponent does
better and fits 99.955% of the data. However, the extreme tail of the
distribution deviates upward even from the power-law fit and exhibits a
dramatic "runaway" behavior. The onset of the runaway regime is revealed
macroscopically as the paper garners 1000-1500 citations, however the
microscopic measurements of autocorrelation in citation rates are able to
predict this behavior in advance.Comment: 6 pages, 5 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