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Published in:
2010 | OriginalPaper | Chapter
Microscopic and kinetic models in financial markets
Authors : Stephane Cordier, Dario Maldarella, Lorenzo Pareschi, Cyrille Piatecki
Published in: Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences
Publisher: Birkhäuser Boston
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We review different microscopic and kinetic models of financial markets which have been developed by economists, physicists, and mathematicians in the last years. We first give a summary of the microscopic models and then introduce the corresponding kinetic equations. Our selective review outlines the main ingredients of some influential models of multiagent dynamics in financial markets like Levy, Levy, and Solomon (Economics Letters, 45, 1994) and Lux and Marchesi (International Journal of Theoretical and Applied Finance, 3, 2000). The introduction of kinetic equations permits to study the asymptotic behavior of the wealth and the price distributions and to characterize the regimes of lognormal behavior and the ones with power-law tails.