From a market of dreamers to economical shocks

Over the past years an intense work has been undertaken to understand the origin of the crashes and bubbles of financial markets. The explanations of these crashes have been grounded on the hypothesis of behavioral and social correlations between the agents in interacting particle models or on a feedback of the stock prices on trading behaviors in mean-field models (here bubbles and crashes are seen as collective hysteria). In this paper, we will introduce a market model as a particle system with no other interaction between the agents than the fact that to be able to sell, somebody must be willing to buy and no feedback of the price on their trading behavior. We will show that this model crashes in finite estimable time. Although the age of the market does not appear in the price dynamic the population of traders taken as a whole system is maturing towards collapse. The wealth distribution among the agents follows the second law of thermodynamics and with probability one an agent (or a minority of agents) will accumulate a large portion of the total wealth, at some point this disproportion in the wealth distribution becomes unbearable for the market leading to its collapse. We believe that the origin of the collapse in our model could be of some relevance in understanding long-term economic cycles such as the Kondratiev cycle.