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Mesoscopic modelling of financial markets

Author

Listed:
  • 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)

  • Cyrille Piatecki

    () (LEO - Laboratoire d'économie d'Orleans - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Stéphane Cordier & Lorenzo Pareschi & Cyrille Piatecki, 2008. "Mesoscopic modelling of financial markets," Working Papers hal-00288167, HAL.
  • Handle: RePEc:hal:wpaper:hal-00288167
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00288167
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