Related papers: Financial Market Dynamics: Superdiffusive or not?
The shape and tails of partial distribution functions (PDF) for a climatological signal, i.e. the El Nino SOI and the turbulent nature of the ocean-atmosphere variability are linked through a model encompassing Tsallis nonextensive…
A justification of the Basel liquidity formula for risk capital in the trading book is given under the assumption that market risk-factor changes form a Gaussian white noise process over 10-day time steps and changes to P&L are linear in…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
We study the probability distribution $Q(n,t)$ of $n(t)$, the fraction of spins unflipped till time $t$, in a Ising chain with ferromagnetic interactions. The distribution shows a peak at $n=n_{max}$ and in general is non-Gaussian and…
We studied the effects of the Tsallis distribution on the transverse momentum fluctuation in high energy collisions. The parton-hadron duality and the Bose-Einstein type correlation between partons were assumed. The fluctuation was…
We present an analysis of a time series of a wind strength measurements recorded at Florence airport in the period October 2002 - March 2003. The data were taken simultaneously by two runway head anemometers, located at a distance of 900 m,…
A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback.…
We proposed the agent-based model of financial markets where agents (or traders) are represented by three-state spins located on the plane lattice or social network. The spin variable represents only the individual opinion (advice) that…
In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes…
We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…
This paper investigates the optimal selection of portfolios for power utility maximizing investors in a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from…
Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases -- in order to uncover their key features -- we have to turn to empirical methods, one of which was recently…
In Statistical Mechanics, Tsallis distributions were apparently conceived in connection with systems presenting long--range interactions. In fact, they were observed in numerical computations for models of such a type, as occurring in the…
This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in…
We report the results of a numerical investigation, performed in the frame of dynamical systems' theory, for a realistic model of a ionic crystal for which, due to the presence of long--range Coulomb interactions, the Gibbs distribution is…
In 1988, Constantino Tsallis proposed an extension of the Boltzmann statistical mechanics by postulating a new entropy formula, $S_q = k_B\ln_q W$, where $W$ is the number of microstates accessible to the system, and $\ln_q$ defines a…
We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has $L^1$ norm close to one and power law tail of the form $x^{-(1+\alpha)}$, with $\alpha\in(0,1)$. We in particular prove that…
An ion in a radiofrequency ion trap interacting with a buffer gas of ultracold neutral atoms is a driven dynamical system which has been found to develop a non-thermal energy distribution with a power law tail. The exact analytical form of…