Bubbles and Absence of Crashes : A Multi-Agent-Based Simulation

It is empirically noticeable that bubbles do not burst but deflate over time. This paper brings some theoretical foundations to this observation. Using multi-agent-based simulations, the limited-arbitrage theory of the risk of synchronisation and a measure of bubble crashes, it is possible to demonstrate that bubbles deflate. The agents are not able to synchronise themselves enough to remove instantaneously the mispricing. This result is robust to the presence of a negative shock which could act as an exogenous signal, the agents underreact to a decrease of the fundamental value. Nevertheless, it exists some favourable conditions for enhancing the synchronisation and speeding up the convergence of the price to the fundamental value. Especially, the paper investigates the impact of the short-selling and borrowing constraints, the risk aversion, the wealth and the gap between the fundamental value and the price