Microscopic and kinetic models in financial markets

We review dierent microscopic and kinetic models of nancial markets which have been developed by economists, physicists and mathematicians in the last years. We rst give a summary of the microscopic models and then introduce the corresponding kinetic equations. Our selective review outlines the main ingredients of some in uential models of multi-agent dynamics in nancial markets like Levy-Levy-Solomon [24] and Lux-Marchesi [29]. 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.