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Quantum Brownian motion model for the stock market

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  • Meng, Xiangyi
  • Zhang, Jian-Wei
  • Guo, Hong

Abstract

It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system—a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg’s uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.

Suggested Citation

  • Meng, Xiangyi & Zhang, Jian-Wei & Guo, Hong, 2016. "Quantum Brownian motion model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 281-288.
    • Handle: RePEc:eee:phsmap:v:452:y:2016:i:c:p:281-288
    DOI: 10.1016/j.physa.2016.02.026
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    References listed on IDEAS

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    Cited by:

    1. Jasmina Jekni'c-Dugi'c & Sonja Radi' c & Igor Petrovi'c & Momir Arsenijevi'c & Miroljub Dugi'c, 2018. "Quantum Brownian oscillator for the stock market," Papers 1901.10544, arXiv.org.
    2. Kein Joe Lau & Yong Kheng Goh & An Chow Lai, 2019. "An empirical study on asymmetric jump diffusion for option and annuity pricing," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-18, May.
    3. Jack Sarkissian, 2016. "Quantum theory of securities price formation in financial markets," Papers 1605.04948, arXiv.org, revised May 2016.
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    5. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).

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