  We propose a heterogeneous agent market model (HAM) in continuous time. The
market is populated by fundamental traders and chartists, who both use simple
linear trading rules. Most of the related literature explores stability, price
dynamics and profitability either within deterministic models or by simulation.
Our novel formulation lends itself to analytic treatment even in the stochastic
case. We prove conditions for the (stochastic) stability of the price process,
and also for the price to mean-revert to the fundamental value. Assuming
stability, we derive analytic formulae on how the population ratios influence
price dynamics and the profitability of the strategies. Our results suggest
that whichever trader type is more present in the market will achieve higher
returns.
