111 research outputs found
A nonextensive approach to the dynamics of financial observables
We present results about financial market observables, specifically returns
and traded volumes. They are obtained within the current nonextensive
statistical mechanical framework based on the entropy
(). More precisely, we
present stochastic dynamical mechanisms which mimic probability density
functions empirically observed. These mechanisms provide possible
interpretations for the emergence of the entropic indices in the time
evolution of the corresponding observables. In addition to this, through
multi-fractal analysis of return time series, we verify that the dual relation
is numerically satisfied, and being
associated to the probability density function and to the sensitivity to
initial conditions respectively. This type of simple relation, whose
understanding remains ellusive, has been empirically verified in various other
systems.Comment: Invited paper to appear in special issue of Eur. Phys. J. B dedicated
to econophysics, edited by T. Di Matteo and T. Aste. 7 page
Markov properties of high frequency exchange rate data
We present a stochastic analysis of a data set consisiting of 10^6 quotes of
the US Doller - German Mark exchange rate. Evidence is given that the price
changes x(tau) upon different delay times tau can be described as a Markov
process evolving in tau. Thus, the tau-dependence of the probability density
function (pdf) p(x) on the delay time tau can be described by a Fokker-Planck
equation, a gerneralized diffusion equation for p(x,tau). This equation is
completely determined by two coefficients D_{1}(x,tau) and D_{2}(x,tau) (drift-
and diffusion coefficient, respectively). We demonstrate how these coefficients
can be estimated directly from the data without using any assumptions or models
for the underlying stochastic process. Furthermore, it is shown that the
solutions of the resulting Fokker-Planck equation describe the empirical pdfs
correctly, including the pronounced tails.Comment: 29 pages, 19 eps figures, misprints corrected, under consideration
for publication in Physica
Carbon allocation and carbon isotope fluxes in the plant-soil-atmosphere continuum: a review
The terrestrial carbon (C) cycle has received increasing interest over the past few decades, however, there is still a lack of understanding of the fate of newly assimilated C allocated within plants and to the soil, stored within ecosystems and lost to the atmosphere. Stable carbon isotope studies can give novel insights into these issues. In this review we provide an overview of an emerging picture of plant-soil-atmosphere C fluxes, as based on C isotope studies, and identify processes determining related C isotope signatures. The first part of the review focuses on isotopic fractionation processes within plants during and after photosynthesis. The second major part elaborates on plant-internal and plant-rhizosphere C allocation patterns at different time scales (diel, seasonal, interannual), including the speed of C transfer and time lags in the coupling of assimilation and respiration, as well as the magnitude and controls of plant-soil C allocation and respiratory fluxes. Plant responses to changing environmental conditions, the functional relationship between the physiological and phenological status of plants and C transfer, and interactions between C, water and nutrient dynamics are discussed. The role of the C counterflow from the rhizosphere to the aboveground parts of the plants, e.g. via CO<sub>2</sub> dissolved in the xylem water or as xylem-transported sugars, is highlighted. The third part is centered around belowground C turnover, focusing especially on above- and belowground litter inputs, soil organic matter formation and turnover, production and loss of dissolved organic C, soil respiration and CO<sub>2</sub> fixation by soil microbes. Furthermore, plant controls on microbial communities and activity via exudates and litter production as well as microbial community effects on C mineralization are reviewed. A further part of the paper is dedicated to physical interactions between soil CO<sub>2</sub> and the soil matrix, such as CO<sub>2</sub> diffusion and dissolution processes within the soil profile. Finally, we highlight state-of-the-art stable isotope methodologies and their latest developments. From the presented evidence we conclude that there exists a tight coupling of physical, chemical and biological processes involved in C cycling and C isotope fluxes in the plant-soil-atmosphere system. Generally, research using information from C isotopes allows an integrated view of the different processes involved. However, complex interactions among the range of processes complicate or currently impede the interpretation of isotopic signals in CO<sub>2</sub> or organic compounds at the plant and ecosystem level. This review tries to identify present knowledge gaps in correctly interpreting carbon stable isotope signals in the plant-soil-atmosphere system and how future research approaches could contribute to closing these gaps
The dynamics of financial stability in complex networks
We address the problem of banking system resilience by applying
off-equilibrium statistical physics to a system of particles, representing the
economic agents, modelled according to the theoretical foundation of the
current banking regulation, the so called Merton-Vasicek model. Economic agents
are attracted to each other to exchange `economic energy', forming a network of
trades. When the capital level of one economic agent drops below a minimum, the
economic agent becomes insolvent. The insolvency of one single economic agent
affects the economic energy of all its neighbours which thus become susceptible
to insolvency, being able to trigger a chain of insolvencies (avalanche). We
show that the distribution of avalanche sizes follows a power-law whose
exponent depends on the minimum capital level. Furthermore, we present evidence
that under an increase in the minimum capital level, large crashes will be
avoided only if one assumes that agents will accept a drop in business levels,
while keeping their trading attitudes and policies unchanged. The alternative
assumption, that agents will try to restore their business levels, may lead to
the unexpected consequence that large crises occur with higher probability
Turbulent luminance in impassioned van Gogh paintings
We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation
How to quantify deterministic and random influences on the statistics of the foreign exchange market
It is shown that prize changes of the US dollar - German Mark exchange rates
upon different delay times can be regarded as a stochastic Marcovian process.
Furthermore we show that from the empirical data the Kramers-Moyal coefficients
can be estimated.
Finally, we present an explicite Fokker-Planck equation which models very
precisely the empirical probabilitiy distributions.Comment: 3 figure
Elements for a Theory of Financial Risks
Estimating and controlling large risks has become one of the main concern of
financial institutions. This requires the development of adequate statistical
models and theoretical tools (which go beyond the traditionnal theories based
on Gaussian statistics), and their practical implementation. Here we describe
three interrelated aspects of this program: we first give a brief survey of the
peculiar statistical properties of the empirical price fluctuations. We then
review how an option pricing theory consistent with these statistical features
can be constructed, and compared with real market prices for options. We
finally argue that a true `microscopic' theory of price fluctuations (rather
than a statistical model) would be most valuable for risk assessment. A simple
Langevin-like equation is proposed, as a possible step in this direction.Comment: 22 pages, to appear in `Order, Chance and Risk', Les Houches (March
1998), to be published by Springer/EDP Science
Size limiting in Tsallis statistics
Power law scaling is observed in many physical, biological and
socio-economical complex systems and is now considered as an important property
of these systems. In general, power law exists in the central part of the
distribution. It has deviations from power law for very small and very large
step sizes. Tsallis, through non-extensive thermodynamics, explained power law
distribution in many cases including deviation from the power law, both for
small and very large steps. In case of very large steps, they used heuristic
crossover approach. In real systems, the size is limited and thus, the size
limiting factor is important. In the present work, we present an alternative
model in which we consider that the entropy factor q decreases with step size
due to the softening of long range interactions or memory. This explains the
deviation of power law for very large step sizes. Finally, we apply this model
for distribution of citation index of scientists and examination scores and are
able to explain the entire distribution including deviations from power law.Comment: 22 pages, 8 figure
Volatile Decision Dynamics: Experiments, Stochastic Description, Intermittency Control, and Traffic Optimization
The coordinated and efficient distribution of limited resources by individual
decisions is a fundamental, unsolved problem. When individuals compete for road
capacities, time, space, money, goods, etc., they normally make decisions based
on aggregate rather than complete information, such as TV news or stock market
indices. In related experiments, we have observed a volatile decision dynamics
and far-from-optimal payoff distributions. We have also identified ways of
information presentation that can considerably improve the overall performance
of the system. In order to determine optimal strategies of decision guidance by
means of user-specific recommendations, a stochastic behavioural description is
developed. These strategies manage to increase the adaptibility to changing
conditions and to reduce the deviation from the time-dependent user
equilibrium, thereby enhancing the average and individual payoffs. Hence, our
guidance strategies can increase the performance of all users by reducing
overreaction and stabilizing the decision dynamics. These results are highly
significant for predicting decision behaviour, for reaching optimal behavioural
distributions by decision support systems, and for information service
providers. One of the promising fields of application is traffic optimization.Comment: For related work see http://www.helbing.or
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