Il modello di Stigler: finestra competitiva, strategie di mercato e auto-organizzazione

The evolution of prices in markets results from the interaction of traders which submit orders to buy or sell. An order book is a list that contains orders sent to a market for a particular commodity or a financial instrument. Orders enter and quit the order book following rules that depends on the particular market. Maybe the most simple and famous order book model is the one named after Stigler. It is defined by a Markovian dynamics where buy and sell orders are placed at random within a price range and a pair of buy-sell orders is cancelled any time a sell order is placed on the left of a buy order. In spite of its simple definition the Stigler model has interesting features: one of these is that the dynamics self-organize to criticality. Indeed the Stigler model is closely related to the Bak-Sneppen model and queueing models with priority which are also known to show self-organized criticality. In the Stigler model self-organization is related to the existence of a competitive window, meaning that in the long run only orders in a restricted price range are executed. The aim of the thesis is to study through probability/complex system tools and simulations the behavior of the Stigler model.