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Mesoscopic Modelling of Financial Markets

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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 (Levy et al. in Econ. Lett. 45:103–111, 1994; Levy et al. in Microscopic Simulation of Financial Markets: From Investor Behavior to Market Phenomena, Academic Press, San Diego, 2000) 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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Authors and Affiliations

  1. MAPMO, (UMR 6628) Fédération Denis Poisson, (FR 2964), Université d’Orléans and CNRS, BP 6759, 45067, Orléans cedex 2, France

    Stephane Cordier

  2. Department of Mathematics and CMCS, University of Ferrara, Via Machiavelli 35, 44100, Ferrara, Italy

    Lorenzo Pareschi

  3. Laboratoire d’Economie d’Orléans (LEO) UMR 6221, University of Orléans and CNRS, 45067, Orléans, France

    Cyrille Piatecki

Authors
  1. Stephane Cordier
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  2. Lorenzo Pareschi
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  3. Cyrille Piatecki
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Correspondence to Lorenzo Pareschi.

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Cordier, S., Pareschi, L. & Piatecki, C. Mesoscopic Modelling of Financial Markets. J Stat Phys 134, 161–184 (2009). https://doi.org/10.1007/s10955-008-9667-z

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  • DOI: https://doi.org/10.1007/s10955-008-9667-z

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