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Kinetic model of wealth distribution by trading stocks with geometric brownian motion

Author

Listed:
  • Ryosuke Yano

    (Tokio Marine dR Co., Ltd., Otemachi 1-5-1, Chiyoda-ku, Tokyo 100-0004, Japan)

  • Hisayasu Kuroda

    (Department of Information Technology, University of Ehime, 3 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan)

Abstract

In this paper, we consider the wealth distribution obtained by trading (buying–selling) stocks whose prices follow the geometric Brownian motion (GBM), when both number of the ticker symbol of the stock and maximum number of the traded stock are limited to unity. The binary exchange of the cash and stock between two agents is expressed with the Boltzmann-type kinetic equation. The distribution function of the number of the agents with the specific number of the stock or specific amount of the cash can be demonstrated, theoretically, when the price of the stock is constant. The distribution function of the number of the agents with the specific amount of the total asset can be approximated by Γ-distribution, when the price of the stock follows the GBM. Finally, the rule in the binary-exchange-game approximates the distribution function of the number of the agents with the specific amount of the total asset to the Feller–Pareto-like distribution at the high wealth tail.

Suggested Citation

  • Ryosuke Yano & Hisayasu Kuroda, 2021. "Kinetic model of wealth distribution by trading stocks with geometric brownian motion," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(12), pages 1-25, December.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:12:n:s0129183122500012
    DOI: 10.1142/S0129183122500012
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