Three-state herding model of the financial markets

We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description exhibiting sophisticated statistical features. Along with power-law probability density function of the absolute returns we are able to reproduce the fractured power spectral density, which is observed in the high-frequency financial market data. Given example of consistent agent-based and stochastic modeling will provide background for the further developments in the research of complex social systems.Comment: 11 pages, 3 figure

Control of the socio-economic systems using herding interactions

Collective behavior of the complex socio-economic systems is heavily influenced by the herding, group, behavior of individuals. The importance of the herding behavior may enable the control of the collective behavior of the individuals. In this contribution we consider a simple agent-based herding model modified to include agents with controlled state. We show that in certain case even the smallest fixed number of the controlled agents might be enough to control the behavior of a very large system.Comment: 8 pages, 3 figure