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15 juin 2008
- handle: 10670/1.325rak
- hal: hal-00288167
info:eu-repo/semantics/OpenAccess
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wealth distribution power-law tails stock market self-similarity kinetic equations. kinetic equationsCiter ce document
Stéphane Cordier et al., « Mesoscopic modelling of financial markets », HAL-SHS : économie et finance, ID : 10670/1.325rak
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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.