Mesoscopic modelling of financial markets
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1009.2743.
Date of creation: Sep 2010
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Publication status: Published in Journal of Statistical Physics, 134, 1, (2009), 161-184
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-25 (All new papers)
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