金澤輝代士 東工大助教, 26 Oct 2018

Date&Time: October 26 (Fri) 2018, 14:00-

Venue: Kyoto University Katsura Campus A4-115

Speaker: Dr Kiyoshi Kanazawa (Tokyo Institute of Technology)

Title: Statistical mechanics of financial Brownian motion: kinetic theory from microscopic dynamics

Abstract:
Kinetic theory is a landmark of statistical physics and is applicable to reveal the physical Brownian motion from first principles. In this framework, the Boltzmann and Langevin equations are systematically derived from the Newtonian dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy [1,2]. In light of this success, it is natural to apply this methodology to social science beyond physics, such as to finance. In this presentation, we apply kinetic theory to financial Brownian motion [3,4] with the empirical support by detailed high-frequency data analysis of a foreign exchange (FX) market.
We first show our data analysis to identify the microscopic dynamics of high-frequency traders (HFTs). By tracking trajectories of all traders individually, we characterize the dynamics of HFTs from the viewpoint of trend-following. We then introduce a microscopic model of FX traders incorporating with the trend following law. We apply the mathematical formulation of kinetic theory to the microscopic model for coarse-graining; Boltzmann-like and Langevin-like equations are derived via a generalized BBGKY hierarchy. We perturbatively solve these equations to show the consistency between our microscopic model and real data. Our work highlights the potential power of statistical physics in understanding the financial market dynamics from their microscopic dynamics.

References
[1] S. Chapman, T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, (Cambridge University Press, Cambridge, England, 1970).
[2] N. G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd ed. (Elsevier, Amsterdam, 2007).
[3] K. Kanazawa, T. Sueshige, H. Takayasu, M. Takayasu, Phys. Rev. Lett. 120, 138301 (2018).
[4] K. Kanazawa, T. Sueshige, H. Takayasu, M. Takayasu, Phys. Rev. E (in press, arXiv:1802.05993).

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