Related papers: Long-Range Dependence in Financial Markets: a Movi…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process,…
We have shown, in a series of articles, that a classical description of a large number of economic agents can be replaced by a statistical fields formalism. To better understand the accumulation and allocation of capital among different…
Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
We present a mathematical model of a market with $m$ shares traded across $n$ investor groups, each one with similar motivations and trading strategies. The market of each asset consists of a fixed amount of cash and shares (no additions…
Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in…
Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose covariance depends on the so-called Hurst parameter $H\in…
In this paper, the diffusion entropy technique is applied to investigate the scaling behavior of stride interval fluctuations of human gait. The scaling behavior of the stride interval of human walking at normal, slow and fast rate are…
This paper suggests that business cycles may be a manifestation of coupled real economy and stock market dynamics and describes a mechanism that can generate economic fluctuations consistent with observed business cycles. To this end, we…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…
We propose an information-theoretical measure, the \textit{relative cluster entropy} $\mathcal{D_{C}}[P \| Q] $, to discriminate among cluster partitions characterised by probability distribution functions $P$ and $Q$. The measure is…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
Many simple natural phenomena are characterized by complex motion that appears random at first glance, but that often displays underlying patterns and behavior that can be clustered in groups. The movement of small pieces of paper falling…
A fundamental question in nonequilibrium statistical physics is whether effective equilibrium behavior can emerge at coarse-grained scales in strongly driven systems. Here, we investigate this question in the context of human mobility by…
A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is investigated on the Chinese stock market using mean-variance analysis, fluctuation analysis and their generalizations to…
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The…
We study the functional link between the Hurst parameter and the Normalized Total Wavelet Entropy when analyzing fractional Brownian motion (fBm) time series--these series are synthetically generated. Both quantifiers are mainly used to…
Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here we make use of this data by investigating fluctuations in yearly usage frequencies of specific words…
Behavior of systems that are functions of anticipated behavior of other systems, whose own behavior is also anticipatory but homeostatic and determined by hierarchical ordering, which changes over time, of sets of possible environments that…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…