Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model

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Abstract
Following the concept of "adaptively rational equilibrium", Brock and Hommes establish a simple present discounted value asset-pricing model with heterogeneous beliefs. Agents adapt their beliefs over time by choosing from different predictors or expectations functions, based upon their past performance as measured by realised profits. As the intensity of choice to switch predictors increases, they have observed several bifurcation routes to complicated asset-price fluctuations. In this paper we extend this model to incorporate different risk attitudes of different types of investors and allow for more sophisticated learning schemes. Using both bifurcation theory and numerical analysis, we investigate the effects on the dynamics of the model of different risk aversion coefficients and different learning schemes. We also systematically investigate the effect of external noise on the system. We find that the resulting dynamical behaviour is considerably enriched and has some significant differences compared to the original Brock-Hommes analysis.
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