Long scale evolution of a nonlinear stochastic dynamic system for modeling market price bubbles

This Letter investigates the stochastic dynamics of a simplified agent-based microscopic model describing stock market evolution. Our mathematical model includes a stochastic market and a sealed-bid double auction. The dynamics of the model are determined by the game of two types of traders: (i) `intelligent' traders whose strategy is based on nonlinear technical data analysis <sup>1</sup> and (ii) `random' traders that act without a consistent strategy. We demonstrate the effect of time-scale separations on the market dynamics. We study the characteristics of the market relaxation in response to perturbations caused by large cash flows generated between these two groups of traders. We also demonstrate that our model exhibits the formation of a price bubble ² and the subsequent transition to a bear market ³.

Bear market - a macroscopically long stage of a market evolution when the stock price declines significantly, 15% or more.