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Pré-Publication, Document De Travail Année : 2008

Mesoscopic modelling of financial markets

Résumé

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.
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Dates et versions

hal-00288167 , version 1 (15-06-2008)

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  • HAL Id : hal-00288167 , version 1

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Stéphane Cordier, Lorenzo Pareschi, Cyrille Piatecki. Mesoscopic modelling of financial markets. 2008. ⟨hal-00288167⟩
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