In this work we essentially reinterpreted the Sieczka-Ho{\l}yst (SH) model to make it more suited for description of real markets. For instance, this reinterpretation made it possible to consider agents as crafty. These agents encourage their neighbors to buy some stocks if agents have an...

We prove that the refined approach -- our extension of the Yakovenko et al. formalism -- is universal in the sense that it describes well both household incomes in the European Union and the individual incomes in the United States for social classes of any income. This formalism allowed the...

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that...

Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income) classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker–Planck counterpart, we derived...

The one-dimensional continuous-time Weierstrass flights (CTWF) model is considered in the framework of the nonseparable continuous-time random walks formalism (CTRW). A novel spatio-temporal coupling is introduced by assuming that in each scale the probability density for the flight and for...

We analysed discrete and continuous Weierstrass–Mandelbrot representations of the Lévy flights occasionally interrupted by spatial localizations. We chose the discrete representation to easily detect by Monte Carlo simulation which stochastic quantity could be a candidate for describing the...

In this work we extend the recently considered toy model of Weierstrass or Lévy walks with varying velocity of the walker (Quantitative Finance 3 (2003) 201; Chem. Phys. 284 (2002) 481; Comp. Phys. Comm. 147 (2002) 565; Phys. A 264 (1999) 84; Phys. A 264 (1999) 107) by introducing a more realistic...

The paper consists of two parts: (i) the empirical one where the non-linear, long-term autocorrelations present in high-frequency data extracting from the Warsaw Stock Exchange were analyzed and (ii) theoretical one where predictions of our model (Quantitative Finance 3 (2003) 201; Physica A...

We proposed the agent-based model of financial markets where agents (or traders) are represented by three-state spins located on the plane lattice or social network. The spin variable represents only the individual opinion (advice) that each trader gives to his nearest neighbors. In the model...

We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily time horizon before and after its well defined local maxima of the cusp-like shape decorated with oscillations. The rising and falling paths of the index peaks can be described by the Mittag-Leffler function superposed...