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We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come.…
Agent-based models help explain stock price dynamics as emergent phenomena driven by interacting investors. In this modeling tradition, investor behavior has typically been captured by two distinct mechanisms -- learning and heterogeneous…
This paper is the first of a series of short articles that explore the efficiency of major cryptocurrency markets. A number of statistical tests and properties of statistical distributions will be used to assess if cryptocurrency markets…
Inspired by the recent literature on aggregation theory, we aim at relating the long range correlation of the stocks return volatility to the heterogeneity of the investors' expectations about the level of the future volatility. Based on a…
We describe a simple model for speculative trading based on adaptive behavior of economic agents.The adaptive behavior is expressed through a feedback mechanism for changing agents' stock-to-bond ratios, depending on the past performance of…
A perspective is taken on the intangible complexity of economic and social systems by investigating the underlying dynamical processes that produce, store and transmit information in financial time series in terms of the \textit{moving…
A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. We focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a…
One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate.…
In complex financial systems, the sector structure and volatility clustering are respectively important features of the spatial and temporal correlations. However, the microscopic generation mechanism of the sector structure is not yet…
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market…
We investigate the large-fluctuation 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 the large fluctuations is characterized by…
This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of…
The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression…
We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an exponentially truncated power-law, similar to…
Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being…
For the pedestrian observer, financial markets look completely random with erratic and uncontrollable behavior. To a large extend, this is correct. At first approximation the difference between real price changes and the random walk model…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…