A Simple Micro-Model of Market Dynamics Part I: The "Homogenous Agents" Deterministic Limit

In this paper we present a simple agent based model aimed to the qualitative description of some ``stylized facts'' typical of financial markets. The framework is a simple two assets model: a riskless bond, with a constant riskless return and a risky stock, paying constant dividends. Both the riskless rate of return and the dividends process are assumed known to the agents. Starting from aggregate excess demand the risky asset price is fixed via Walrasian auction. The market participants are speculators described as myopic utility maximizer and are embedded with limited forecasting ability. The exact expressions of the utility function and the forecasting procedure are chosen in order to admit a simple analytic treatment of the market dynamics in the deterministic limit of homogeneous agents. However, a short discussion of the effect of different choices is proposed. We find that in the deterministic limit the model posses many ``phases''. In particular, the no-arbitrage ``fundamental'' price can emerge as a stable fixed point, while for different parameterizations the market shows chaotic dynamics with speculative bubbles and crashes.