283 research outputs found
The Tenth Article of Ettore Majorana
This year is the centenary of the birth of Ettore Majorana, one of the major
Italian physicists of all times. In this note we briefly sketch a few
biographical details about Ettore Majorana and introduce and discuss the main
points of Majorana's 10th article. In his article Majorana explicitly considers
quantum mechanics as an irreducible statistical theory because the theory is
not able to describe the time evolution of a single particle or atom in a
precise environment at a deterministic level. This lack of determinism at the
level of an elementary physical system motivated him to suggest a formal
analogy between statistical laws observed in physics and in the social
sciences. We hope the occasion of the centenary of the birth of Ettore Majorana
will be useful to remember and to reconsider not only his exceptional
achievements in theoretical physics but also his fresh and original views on
the role of statistical laws in physics and in other disciplines such as the
social sciences.Comment: 3 pages, to appear in Europhysics News 37/4 July/August 200
Hierarchical Structure in Financial Markets
I find a topological arrangement of stocks traded in a financial market which
has associated a meaningful economic taxonomy. The topological space is a graph
connecting the stocks of the portfolio analyzed. The graph is obtained starting
from the matrix of correlation coefficient computed between all pairs of stocks
of the portfolio by considering the synchronous time evolution of the
difference of the logarithm of daily stock price. The hierarchical tree of the
subdominant ultrametric space associated with the graph provides information
useful to investigate the number and nature of the common economic factors
affecting the time evolution of logarithm of price of well defined groups of
stocks.Comment: 11 pages, 3 figures with 7 panel
Symmetry alteration of ensemble return distribution in crash and rally days of financial markets
We select the stocks traded in the New York Stock Exchange and we form a
statistical ensemble of daily stock returns for each of the trading days of
our database from the stock price time series. We study the ensemble return
distribution for each trading day and we find that the symmetry properties of
the ensemble return distribution drastically change in crash and rally days of
the market. We compare these empirical results with numerical simulations based
on the single-index model and we conclude that this model is unable to explain
the behavior of the market in extreme days.Comment: 4 pages, 4 figure
Empirical properties of the variety of a financial portfolio and the single-index model
We investigate the variety of a portfolio of stocks in normal and extreme
days of market activity. We show that the variety carries information about the
market activity which is not present in the single-index model and we observe
that the variety time evolution is not time reversal around the crash days. We
obtain the theoretical relation between the square variety and the mean return
of the ensemble return distribution predicted by the single-index model. The
single-index model is able to mimic the average behavior of the square variety
but fails in describing quantitatively the relation between the square variety
and the mean return of the ensemble distribution. The difference between
empirical data and theoretical description is more pronounced for large
positive values of the mean return of the ensemble distribution. Other
significant deviations are also observed for extreme negative values of the
mean return.Comment: 8 pages, 5 figures, 3 table
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