Market price fluctuations: contact point between agent based approach and stochastic processes

The author presents a contact point between an agent based approach and stochastic processes. Market price fluctuations are approached from three viewpoints: statistical properties of foreign exchange rates (macroscopic); an artificial market (microscopic); and stochastic processes (mesoscopic). A simple artificial market model is introduced and investigated both numerically and analytically. A stochastic process for price dynamics is derived from the artificial market model and its statistical property is exhibited. The study establishes a bridge between an artificial market model and stochastic processes.