Related papers: Universality in DAX index returns fluctuations

We apply an asymmetric version of Kirman's herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a…

We introduce When Alpha Disappears, a paired evaluation benchmark for diagnosing decision-time leakage in financial machine-learning backtests. Rather than treating leakage as a binary property, the benchmark estimates protocol-induced…

We apply the formalism of the continuous time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time…

We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity…

The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…

The Hartman-Watson distribution with density $f_r(t)$ is a probability distribution defined on $t \geq 0$ which appears in several problems of applied probability. The density of this distribution is expressed in terms of an integral…

Let $X=(X_t)$ be a one-dimensional Ornstein-Uhlenbeck process with an initial density function $f$ supported on the positive real-line that is a regularly varying function with exponent $-(1+\eta)$, with $\eta\in (0,1)$. We prove the…

We generalize the recently proposed quantum model for the stock market by Zhang and Huang to make it consistent with the discrete nature of the stock price. In this formalism, the price of the stock and its trend satisfy the generalized…

This article presents an important theorem, which shows that from the moments of the standard normal distribution one can generate density functions originating a family of models. Additionally, we discussed that different random variable…

We provide evidence that cumulative distributions of absolute normalized returns for the $100$ American companies with the highest market capitalization, uncover a critical behavior for different time scales $\Delta t$. Such cumulative…

The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The…

We study asymptotics of the spectral measure of a randomly chosen partial automorphism of a rooted tree. To every partial automorphism $x$ we assign its action matrix $A_x$. It is shown that the uniform distribution on eigenvalues of $A_x$…

This paper considers estimation of the predictive density for a normal linear model with unknown variance under alpha-divergence loss for -1 <= alpha <= 1. We first give a general canonical form for the problem, and then give general…

We report major advances in the research program initiated in "Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities" (J. Phys. A, 45, 095305 [2012]). A highly succinct separability…

A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…

In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…

We introduce a non-parametric method to recover physical probability distributions of asset returns based on their European option prices and some other sparse parametric information. Thus the main problem is similar to the one considered…

We introduce a two-parameter family of probability distributions, indexed by $\beta/2 = \theta > 0$ and $K \in \mathbb{Z}_{\geq 0}$, that are called $\beta$-Krawtchouk corners processes. These measures are related to Jack symmetric…

The aim of this work is to provide bounds connecting two probability measures of the same event using R\'enyi $\alpha$-Divergences and Sibson's $\alpha$-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence…