相关论文: Small scale behavior of financial data

Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a…

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models are now available, their…

Linear causal analysis is central to a wide range of important application spanning finance, the physical sciences, and engineering. Much of the existing literature in linear causal analysis operates in the time domain. Unfortunately, the…

A new model of search based on stochastic resetting is introduced, wherein rate of resets depends explicitly on time elapsed since the beginning of the process. It is shown that rate inversely proportional to time leads to paradoxical…

We review a resent {\em time-dependent} performance measure for economical time series -- the (optimal) investment horizon approach. For stock indices, the approach shows a pronounced gain-loss asymmetry that is {\em not} observed for the…

Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…

Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…

The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

The time series theory is set in this work under the domain of general elliptically contoured distributions. The advent of a time series approach that is in accordance with the expected reality of dependence between errors, transfers the…

Small random perturbations may have a dramatic impact on the long time evolution of dynamical systems, and large deviation theory is often the right theoretical framework to understand these effects. At the core of the theory lies the…

In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span $\Delta t$, say one week or one year. This measures how well (or…

We analyse the dependence of stock return cross-correlations on the sampling frequency of the data known as the Epps effect: For high resolution data the cross-correlations are significantly smaller than their asymptotic value as observed…

We empirically analyze the reversion of financial market trends with time horizons ranging from minutes to decades. The analysis covers equities, interest rates, currencies and commodities and combines 14 years of futures tick data, 30…

A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus…

We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in…

We study a simple run-and-tumble random walk whose switching frequency from run mode to tumble mode and the reverse depend on a stochastic signal. We consider a particularly sharp, step-like dependence, where the run to tumble switching…

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling…

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…