74 research outputs found
Langevin processes, agent models and socio-economic systems
We review some approaches to the understanding of fluctuations in some models
used to describe socio and economic systems. Our approach builds on the
development of a simple Langevin equation that characterises stochastic
processes. This provides a unifying approach that allows first a
straightforward description of the early approaches of Bachelier. We generalise
the approach to stochastic equations that model interacting agents. Using a
simple change of variable, we show that the peer pressure model of Marsilli and
the wealth dynamics model of Solomon are closely related. The methods are
further shown to be consistent with a global free energy functional that
invokes an entropy term based on the Boltzmann formula. A more recent approach
by Michael and Johnson maximised a Tsallis entropy function subject to simple
constraints. We show how this approach can be developed from an agent model
where the simple Langevin process is now conditioned by local rather than
global noise. The approach yields a BBGKY type hierarchy of equations for the
system correlation functions. Of especial interest is that the results can be
obtained from a new free energy functional similar to that mentioned above
except that a Tsallis like entropy term replaces the Boltzmann entropy term. A
mean field approximation yields the results of Michael and Johnson. We show how
personal income data for Brazil, the US, Germany and the UK, analysed recently
by Borgas can be qualitatively understood by this approach.Comment: 1 figur
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
Stochastic Multiplicative Processes for Financial Markets
We study a stochastic multiplicative system composed of finite asynchronous
elements to describe the wealth evolution in financial markets. We find that
the wealth fluctuations or returns of this system can be described by a walk
with correlated step sizes obeying truncated Levy-like distribution, and the
cross-correlation between relative updated wealths is the origin of the
nontrivial properties of returns, including the power law distribution with
exponent outside the stable Levy regime and the long-range persistence of
volatility correlations.Comment: 12 pages, 6 figures, to be published in Physica A (Proceedings of
Statphys21 conference
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