The authors are indebted to the anonymous referee for a very detailed and insightful report on an earlier version of this paper that has led to many improvements in the current version. Address correspondence to: Tony He, School of Finance and Economics, University of Technology, Sydney, P.O. Box 123 Broadway, NSW 2007, Australia; e-mail: [email protected]. This paper studies the dynamics of a simple discounted present-value asset-pricing model where agents have different risk attitudes and follow different expectation formation schemes for the price distribution. A market-maker scenario is used as the market-clearing mechanism, in contrast to the more usual Walrasian scenario. In particular, the paper concentrates on models of fundamentalists and trend followers who follow recursive geometric-decay (learning) processes (GDP) with both finite and infinite memory. The analysis depicts how the dynamics are affected by various key elements (or parameters) of the model, such as the adjustment speed of the market maker, the extrapolation rate of the trend followers, the decay rate of the GDP, the lag length used in the learning GDP, and external random factors.