Abstract:
We shall present an overview of current status of modelling the stock market using the models borrowed from statistical physics. From an abstract point of view, we always deal with one-dimensional non-equilibrium systems of interacting particles. New simulations for old models as well as original contributions of the author will be shown, starting from the early Stigler model (1964), through reaction-diffusion models, Genoa artificial stock market, to models of Maslov and Farmer to the schematic Interacting Gaps model. We shall show that the pure models can be clearly classified into several universality classes according to the return-distribution exponent and the Hurst exponent. Several analytical approaches will be presented, essentially all of them relying on some mean-field scheme. Interestingly enough, in some cases the mean-field results coincide with the simulation results for the true one-dimensional system. As a general conclusion, we state that the models of econophysics are still rather far from being satisfactory.