Mesoscopic modelling of financial markets
We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investments alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model 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.
|Date of creation:||15 Jun 2008|
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|Note:||View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00288167/en/|
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