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Mesoscopic modelling of financial markets

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

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    File URL: http://arxiv.org/pdf/1009.2743
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    Paper provided by arXiv.org in its series Papers with number 1009.2743.

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    Date of creation: Sep 2010
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    Publication status: Published in Journal of Statistical Physics, 134, 1, (2009), 161-184
    Handle: RePEc:arx:papers:1009.2743

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    Web page: http://arxiv.org/

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