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Shifted Brownian Fluctuation Game

Author

Listed:
  • Song-Kyoo (Amang) Kim

    (Faculty of Applied Sciences, Macao Polytechnic University, R. de Luis Gonzaga Gomes, Macao SAR, China)

Abstract

This article analyzes the behavior of a Brownian fluctuation process under a mixed strategic game setup. A variant of a compound Brownian motion has been newly proposed, which is called the Shifted Brownian Fluctuation Process to predict the turning points of a stochastic process. This compound process evolves until it reaches one step prior to the turning point. The Shifted Brownian Fluctuation Game has been constructed based on this new process to find the optimal moment of actions. Analytically tractable results are obtained by using the fluctuation theory and the mixed strategy game theory. The joint functional of the Shifted Brownian Fluctuation Process is targeted for transformation of the first passage time and its index. These results enable us to predict the moment of a turning point and the moment of actions to obtain the optimal payoffs of a game. This research adapts the theoretical framework to implement an autonomous trader for value assets including stocks and cybercurrencies.

Suggested Citation

  • Song-Kyoo (Amang) Kim, 2022. "Shifted Brownian Fluctuation Game," Mathematics, MDPI, vol. 10(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1735-:d:818985
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    References listed on IDEAS

    as
    1. Jewgeni H. Dshalalow & Ryszard Syski, 1994. "Lajos Takács and his work," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-23, January.
    2. Moschini, GianCarlo, 2004. "Nash equilibrium in strictly competitive games: live play in soccer," Economics Letters, Elsevier, vol. 85(3), pages 365-371, December.
    3. Song-Kyoo (Amang) Kim, 2020. "A Versatile Stochastic Duel Game," Mathematics, MDPI, vol. 8(5), pages 1-13, May.
    4. Jewgeni H. Dshalalow, 1994. "First excess levels of vector processes," International Journal of Stochastic Analysis, Hindawi, vol. 7, pages 1-8, January.
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    Cited by:

    1. Song-Kyoo (Amang) Kim, 2022. "Versatile Stochastic Two-Sided Platform Models," Mathematics, MDPI, vol. 11(1), pages 1-15, December.

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