Kinetic theory for financial Brownian motion: a microscopic model based on forex data analysis and its mean-field theory

Kinetic theory is a powerful mathematical framework in statistical physics and has been applied to understand physical Brownian motions from their microscopic setups. In light of this success, it is an interesting attempt to extend kinetic theory for various social phenomena beyond physics. In particular, we have focused on its application to financial markets since they exhibit random motions quite similar to physical Brownian motion. In this presentation, we will show our recent kinetic approach (K. Kanazawa et al., PRL 2018; PRE 2018) to financial Brownian motion in the context of high-frequency data analyses. First, we have analyzed trading log data of individual traders, to identify the microscopic dynamics in a forex market. The proposed microscopic model of the financial market is then solved systematically via the kinetic theory: we derive the Liouville equation, the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, the Boltzmann equation, and the Langevin equation for the financial market as a parallel mathematical program to conventional kinetic theory. Our work highlights the potential power of kinetic theory to understand social phenomena from their microscopic dynamics.