EMERGENCE OF POWER-LAW AND TWO-PHASE BEHAVIOR IN FINANCIAL MARKET FLUCTUATIONS

In this paper, we provide an insight into the emergence of power-law and two-phase behavior in the financial market fluctuations by defining an analytical model for time evolution of stock share prices. The defined model can exhibit bimodal behavior in the supply-demand structure of the market. Moreover, it differs from existing Ising-type models. It turns out that the constructed model is a solution of a thermodynamic limit of a Gibbs probability measure when the number of investors and the number of stock shares approaches the infinity. The energy functional of the Gibbs probability measure is derived from the Nash equilibrium of the underlying game.