Asset pricing with a continuum of belief types

The literature on multi-agent models up until recently has been mainly concerned with the price dynamics in a setting where agents are allowed to switch between a finite number of strategies.In reality, however, we would expect a high degree of heterogeneity, such that few belief types will probably be insufficient to model the rich behaviour of price fluctuations observed in real finacial data. Therefore a first important question that arises, is whether an asset pricing model that allows for many trader types is able to generate additional stylized facts in comparison to the few belief type models. Secondly, it would be interesting to investigate the time evolution of the degree of heterogeneity. For example, under what conditions will a small subset of the initial set of belief types eventually attract most of the population of traders. The latter questions are particularly interesting since they provide insight in the behaviour of economic agents in terms of the evolution of the despersion of their beliefs. We introduce a novel class of agent models for asset pricing, in which dispersion of beliefs is modelled by a probability distribution over a continuum of belief parameters. Agents base their strategies on past performance measures. This approach gives rise to prices dynamics in which the distribution of beliefs evolves together with the realised prices. For several classes of beliefs, we show that the dynamics of the probability distribution can be formulated in terms of the evolution of a finite number of characteristic parameters for the probability distribution of beliefs. Both the role of the performance measure and the class of predictors of future prices is examined analytically as well as numerically.