Related papers: Market dynamics immediately before and after finan…
A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear visco-elasticity. Several aftershocks are generated after the main shock owing to the damping of the additional visco-elastic force. Both the…
The elementary theory of aftershocks, being relatively simple mathematically, belongs to the basics of earthquake physics. The paper briefly outlines the concepts and ideas of the theory, provides equations for the relaxation of the source…
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from…
The deactivation coefficient has been introduced for the source that cools down after the mainshock of the earthquake. The deactivation coefficient satisfies two conditions. First, it can be computed from observed aftershock frequency data…
We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for…
Recently, simple differential models of aftershocks have attracted increased attention of researchers at the Institute of Physics of the Earth, Russian Academy of Sciences for their remarkable properties. The shortened Bernoulli equation…
In financial markets, greater volatility is usually considered synonym of greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To…
The earthquake source after the main shock can theoretically be represented as a black box without an entrance. At the output, there is a signal in the form of aftershocks, the frequency of which decreases on average with time according to…
The known Omori law is presented in the form of differential equation that describes the evolution of the aftershock activity. This equation is derived hypothetically with taking into account deactivation of the faults in epicentral zone of…
Cross-sectional signatures of market panic were recently discussed on daily time scales in [1], extended here to a study of cross-sectional properties of stocks on intra-day time scales. We confirm specific intra-day patterns of dispersion…
A part of the seismic time series, in which the Omori law for temporal pattern of aftershocks holds, is refereed to as the Omori regime. Here the properties of correlation between earthquake events both inside and outside of the Omori…
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a…
Using a modified damped harmonic oscillator model equivalent to a model of market dynamics with price expectations, we analyze the reaction of financial markets to shocks. In order to do this, we gather data from indices of a variety of…
A recent model predicting Omori's law giving the number of aftershocks per unit time following an earthquake involves a differential equation analogous to the Friedmann equation of cosmology. The before-shock phase is analogous to an…
The power law of aftershock evolution was proposed by Hirano in 1924 and introduced by Utsu into seismology in the second half of the last century. The Hirano-Utsu law is widely used in studying the relaxation of earthquake source after the…
We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the…
The empirical Bath's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere-Jones [1969] and Console et al. [2003], we show that the…
We exploit a continuous time random walk description of stock prices to obtain a fast and accurate evaluation of their volatility from intraday data. We show that financial markets are usefully described as open physical systems. Indeed we…
We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by…
We study analytically and by numerical simulations the statistics of the aftershocks generated after large avalanches in models of interface depinning that include viscoelastic relaxation effects. We find in all the analyzed cases that the…