Reaction to Extreme Events in a Minimal Agent Based Model

We consider the issue of the overreaction of financial markets to a sudden price change. In particular, we focus on the price and the population dynamics which follows a large fluctuation. In order to investigate these aspects from different perspectives we discuss the known results for empirical data, the Lux-Marchesi model and a minimal agent based model which we have recently proposed. We show that, in this framework, the presence of a overreaction is deeply linked to the population dynamics. In particular, the presence of a destabilizing strategy in the market is a necessary condition to have an overshoot with respect to the exogenously induced price fluctuation. Finally, we analyze how the memory of the agents can quantitatively affect this behavior.