Mesoscopic modelling of financial markets

Stéphane Cordier (), Lorenzo Pareschi () and Cyrille Piatecki ()
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Stéphane Cordier: MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique
Lorenzo Pareschi: Center for Modelling Computing and Statistics, c/o Department of Economy, Institutions and Territory - UniFE - Università degli Studi di Ferrara = University of Ferrara
Cyrille Piatecki: LEO - Laboratoire d'économie d'Orleans [2008-2011] - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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.

Keywords: wealth distribution; power-law tails; stock market; self-similarity; kinetic equations.; kinetic equations (search for similar items in EconPapers)
Date: 2008-06-15
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