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A quantum model for the stock market

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  • Zhang, Chao
  • Huang, Lu

Abstract

Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schrödinger equation for stock price. Based on this theoretical framework, an example of a driven infinite quantum well is considered, in which we use a cosine distribution to simulate the state of stock price in equilibrium. After adding an external field into the Hamiltonian to analytically calculate the wave function, the distribution and the average value of the rate of return are shown.

Suggested Citation

  • Zhang, Chao & Huang, Lu, 2010. "A quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5769-5775.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5769-5775
    DOI: 10.1016/j.physa.2010.09.008
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    References listed on IDEAS

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    7. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.
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    Citations

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    Cited by:

    1. Yaghobipour, S. & Yarahmadi, M., 2018. "Optimal control design for a class of quantum stochastic systems with financial applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 507-522.
    2. Liviu-Adrian Cotfas, 2012. "Finite quantum mechanical model for the stock market," Papers 1208.6146, arXiv.org, revised Sep 2012.
    3. Bikramaditya Ghosh & Krishna MC, 2020. "Econophysical bourse volatility – Global Evidence," Journal of Central Banking Theory and Practice, Central bank of Montenegro, vol. 9(2), pages 87-107.
    4. Pouria Pedram, 2011. "The minimal length uncertainty and the quantum model for the stock market," Papers 1111.6859, arXiv.org, revised Jan 2012.
    5. Jack Sarkissian, 2016. "Spread, volatility, and volume relationship in financial markets and market making profit optimization," Papers 1606.07381, arXiv.org.
    6. 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.
    7. Godinho, Cresus F.L. & Abreu, Everton M.C., 2021. "The analysis of the dynamic optimization problem in econophysics from the point of view of the symplectic approach for constrained systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. Kumar, Sushil & Kumar, Sunil & Kumar, Pawan, 2020. "Diffusion entropy analysis and random matrix analysis of the Indian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    9. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    10. Xiangyi Meng & Jian-Wei Zhang & Jingjing Xu & Hong Guo, 2014. "Quantum spatial-periodic harmonic model for daily price-limited stock markets," Papers 1405.4490, arXiv.org.
    11. Liviu-Adrian Cotfas, 2012. "A finite-dimensional quantum model for the stock market," Papers 1204.4614, arXiv.org, revised Sep 2012.
    12. Meng, Xiangyi & Zhang, Jian-Wei & Xu, Jingjing & Guo, Hong, 2015. "Quantum spatial-periodic harmonic model for daily price-limited stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 154-160.
    13. Jack Sarkissian, 2016. "Quantum theory of securities price formation in financial markets," Papers 1605.04948, arXiv.org, revised May 2016.
    14. Gao, Tingting & Chen, Yu, 2017. "A quantum anharmonic oscillator model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 307-314.
    15. Cotfas, Liviu-Adrian, 2013. "A finite-dimensional quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 371-380.
    16. Pedram, Pouria, 2012. "The minimal length uncertainty and the quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2100-2105.
    17. Kuzu, Erkan & Süsay, Aynur & Tanrıöven, Cihan, 2022. "A model study for calculation of the temperatures of major stock markets in the world with the quantum simulation and determination of the crisis periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    18. Pineiro-Chousa, Juan & Vizcaíno-González, Marcos, 2016. "A quantum derivation of a reputational risk premium," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 304-309.
    19. 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.

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