Ab initio analysis of all income society classes in the European Union

We found a unified formula for description of the household incomes of all society classes, for instance, of those of the European Union in year 2007. This formula is a stationary solution of the threshold Fokker-Planck equation (derived from the threshold nonlinear Langevin one). The formula is more general than the well known that of Yakovenko et al. because it satisfactorily describes not only household incomes of low- and medium-income society classes but also the household incomes of the high-income society class.Comment: Accepted for publication in Acta Physica Polonica A. arXiv admin note: substantial text overlap with arXiv:1301.207

Reinterpretation of Sieczka-Ho{\l}yst financial market model

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 opportunity to sell these stocks. Also, agents encourage them to sell some stocks if agents have an opposite opportunity. Furthermore, in our interpretation price changes respond only to the agents' opinions change. This kind of respond protects the stock market dynamics against the paradox (present in the SH model), where all agents e.g. buy stocks while the corresponding prices remain unchanged. In this work we found circumstances, where distributions of returns (obtained for quite different time scales) either obey power-law or have at least fat tails. We obtained these distributions from numerical simulations performed in the frame of our approach