Economic and financial time series show well defined deviations from the simple Random Walk behavior. These Stylized Facts (SF) consist mainly in the Fat Tails, Volatility Clustering and Arbitrage properties. Agent Based Models (ABM) have been introduced to reproduce them but it is difficult to identify the specific origin of the SF and, in particular, why the system self-organizes in this quasi-critical state. We review the state of the art and introduce a new ABM which focuses on  these questions and permits a clear identification of the origin of the SF and of the self-organization phenomenon. In particular the SF consist in a special case of punctuated finite size effects with respect to the  fluctuations of the number of active agents. We then consider the crucial problem of the self-organization to this quasi-critical state and show specific mechanisms for the development of this phenomenon.

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1. Origin of stylized facts in self-organizing agent based model