The modeling of some internal processes on a stock market. The Agent-Based Model of the Closed Market of the One Commodity with Finite Automata as Participants of the Market

      Аннотация: The behavior of stock market prices as a response on the variation of external conditions is very complicated problem. We begin our investigation of that problem from research of very simple mathematical models of stock market in the periods when variations of a external conditions for the stock market are small. The model of market of one commodity, in which there is in each moment of time the same quantity of goods, the same quantity of money was formulated, researched in this paper. Each participant of the market in the one moment of time can be in one of three statuses: to be buyer, be seller, do not take part in trade in this moment of time, can to change his status, price, by using the personal information about trade in the previous moment of time only. The convergence of trajectory of our system to stationary set of states with average price of trade which is close to some constant was established by series of experiments with computer realization of the model. Some cases of the herd behavior of participants were considered in this investigation. This text can be useful for the scientists, for the students of economics, mathematics.

Ключевые слова: trajectory, closed market, one commodity market, dynamics of prices, stationary set, Mathematical Model, Rational Choice., steady state, stock market, behavior of agents