Equilibria in financial markets with heterogeneous agents: a probabilistic perspective

We analyse financial market models in which agents form their demand for an asset on the basis of their forecasts of future prices and where their forecasting rules may change over time, as a result of the influence of other traders. Agents will switch from one rule to another stochastically, and the price and profits process will reflect these switches. Among the possible rules are “chartist” or extrapolatory rules. Prices can exhibit transient behaviour when chartists predominate. However, if the probability that an agent will switch to being a “chartist” is not too high then the process does not explode. There are occasional bubbles but they inevitably burst. In fact, we prove that the limit distribution of the price process exists and is unique. This limit distribution may be thought of as the appropriate equilibrium notion for such markets. A number of characteristics of financial time series can be captured by this sort of model. In particular, the presence of chartists fattens the tails of the stationary distribution.