Continuous beliefs dynamics

We propose a general framework for studying the evolution ofheterogeneous beliefs in a dynamic feedback setting. Beliefsdistributions are defined on a continuous space representingthe possible strategies agents can choose from. Agents base theirchoices on past performances. As new information becomesavailable strategies are re-evaluated and the beliefsdistribution is updated using a continuous choice model. Thisapproach gives rise to price dynamics in which the beliefsdistribution evolves together with realized prices. Thestatistical properties of the endogenous random pricefluctuations are fully determined by the model. The structure ofthe macroscopic model depends on the class of predictors and onthe performance measure used by the agents. Whenever a well-knowneconometric model is obtained, an economic interpretation of themodel parameters can be given, as is shown here for an ARCHmodel. The approach is illustrated with several examples andempirical applications.