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Mesoscopic modelling of financial markets

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  • S. Cordier
  • L. Pareschi
  • C. Piatecki

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 (Econ. Lett., 45, (1994), 103--111) 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

  • S. Cordier & L. Pareschi & C. Piatecki, 2010. "Mesoscopic modelling of financial markets," Papers 1009.2743, arXiv.org.
    • Handle: RePEc:arx:papers:1009.2743
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