Related papers: Fractal properties, information theory, and market…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
We discuss the role of information entropy on the behaviour of random processes, and how this might take effect in the dynamics of financial market prices. We then go on to show how the Open Quantum Systems approach can be used as a more…
S&P 500 index data sampled at one-minute intervals over the course of 11.5 years (January 1989- May 2000) is analyzed, and in particular the Hurst parameter over segments of stationarity (the time period over which the Hurst parameter is…
We estimate the Hurst parameter $H$ of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of $H$ more difficult since relevant…
A multivariate fractional Brownian motion (mfBm) with component-wise Hurst exponents is used to model and forecast realized volatility. We investigate the interplay between correlation coefficients and Hurst exponents and propose a novel…
The Efficient Market Hypothesis has been a staple of economics research for decades. In particular, weak-form market efficiency -- the notion that past prices cannot predict future performance -- is strongly supported by econometric…
The efficient market hypothesis has far-reaching implications for financial trading and market stability. Whether or not cryptocurrencies are informationally efficient has therefore been the subject of intense recent investigation. Here, we…
Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it…
In its semi-strong form, the Efficient Market Hypothesis (EMH) implies that technical analysis will not reveal any hidden statistical trends via intermarket data analysis. If technical analysis on intermarket data reveals trends which can…
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…
We propose a model for stochastic formation of opinion clusters, modelled by an evolving network, and herd behaviour to account for the observed fat-tail distribution in returns of financial-price data. The only parameter of the model is h,…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
We present a novel approach to describing the microstructure of high frequency trading using two key elements. First we introduce a new notion of informed trader which we starkly contrast to current informed trader models. We describe the…
We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of…
Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…
We consider utility maximization problem for semi-martingale models depending on a random factor $\xi$. We reduce initial maximization problem to the conditional one, given $\xi=u$, which we solve using dual approach. For HARA utilities we…
The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of…
When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic…
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…