Related papers: The $\kappa$-generalised Distribution for Stock Re…
Our purpose is to relate the Fokker-Planck formalism proposed by [Friedrich et al., Phys. Rev. Lett. 84, 5224 (2000)] for the distribution of stock market returns to the empirically well-established power law distribution with an exponent…
Using the Generalised Lotka Volterra (GLV) model adapted to deal with muti agent systems we can investigate economic systems from a general viewpoint and obtain generic features common to most economies. Assuming only weak generic…
In this paper we quantitatively investigate the statistical properties of an ensemble of {\it stock prices}. We selected 1200 stocks traded in the Tokyo Stock Exchange and formed a statistical ensemble of daily stock prices for each trading…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
Distributions exhibiting fat tails occur frequently in many different areas of science. A dynamical reason for fat tails can be a so-called superstatistics, where one has a superposition of local Gaussians whose variance fluctuates on a…
We discuss a family of models expressed by nonlinear differential equation systems describing closed market societies in the presence of taxation and redistribution. We focus in particular on three example models obtained in correspondence…
This note derives the various forms of entropy of systems subject to Olbert distributions (generalized Lorentzian probability distributions known as $\kappa$-distributions) which are frequently observed particularly in high temperature…
In this paper we test computationally the performance of CAPM in an evolutionary setting. In particular we study the stability of wealth distribution in a financial market where some traders invest as prescribed by CAPM and others behave…
We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the…
The growth dynamics of complex systems often exhibit statistical regularities involving power-law relationships. For real finite complex systems formed by countable tokens (animals, words) as instances of distinct types (species, dictionary…
Given $n$ samples of a regular discrete distribution $\pi$, we prove in this article first a serial of SLLNs results (of Dvoretzky and Erd\"{o}s' type) which implies a typical power law when $\pi$ is heavy-tailed. Constructing a (random)…
The generally accepted representation of $\kappa$-distributions in space plasma physics allows for two different alternatives, namely assuming either the temperature or the thermal velocity to be $\kappa$-independent. The present paper aims…
We analyze the statistical dependency structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange's TAQ database. With a copula-based approach, we find that the…
Financial markets are highly non-linear and non-equilibrium systems. Earlier works have suggested that the behavior of market returns can be well described within the framework of non-extensive Tsallis statistics or superstatistics. For…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
For any fixed simple graph $H=(V,E)$ and any fixed $u>0$, we establish the leading order of the exponential rate function for the probability that the number of copies of $H$ in the Erd\H{o}s--R\'enyi graph $G(n,p)$ exceeds its expectation…
Gradually Truncated Power law distribution - Citation of scientists Hari M. Gupta, Jose R. Campanha and Bianca A. Ferrari Unesp - Physics Dpto. - Rio Claro Sao Paulo - Brazil Abstract The number of times, a scientist is cited in other…
We derive the characteristic function of stochastic functionals of a random walk whose position is reset to the origin at random times drawn from a general probability distribution. We analyze the long-time behavior and obtain the temporal…
The emergence of heavy-tailed statistics in complex systems is conventionally attributed to non-local stochastic jumps or non-Markovian memory. Here, we present a one-dimensional random walk where power-law behaviors arise instead from a…
This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock…