%0 Journal Article
%T Mesoscopic modelling of financial markets
%A S. Cordier
%A L. Pareschi
%A C. Piatecki
%J Quantitative Finance
%D 2010
%I arXiv
%R 10.1007/s10955-008-9667-z
%X We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis.
%U http://arxiv.org/abs/1009.2743v1