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 (Levy et al. in Econ. Lett. 45:103-111, 1994; Levy et al. in Microscopic Simulation of Financial Markets: From Investor Behavior to Market Phenomena, Academic Press, San Diego, 2000) 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. © 2009 Springer Science+Business Media, LLC.
Mesoscopic modelling of financial markets
PARESCHI, Lorenzo;
2009
Abstract
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 (Levy et al. in Econ. Lett. 45:103-111, 1994; Levy et al. in Microscopic Simulation of Financial Markets: From Investor Behavior to Market Phenomena, Academic Press, San Diego, 2000) 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. © 2009 Springer Science+Business Media, LLC.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
