The Dynamics of the Linear Random Farmer Model

On the framework of the Linear Farmer's Model, we approach the indeterminacy of agents' behaviour by associating with each agent an unconditional probability for her to be active at each time step. We show that Pareto tailed returns can appear even if value investors are the only strategies on the market and give a procedure for the determination of the tail exponent. Numerical results indicate that the returns' distribution is heavy tailed and volatility is clustered if trading occurs at the zero Lyapunov (critical) point.