IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1204.4614.html
   My bibliography  Save this paper

A finite-dimensional quantum model for the stock market

Author

Listed:
  • Liviu-Adrian Cotfas

Abstract

We present a finite-dimensional version of the quantum model for the stock market proposed in [C. Zhang and L. Huang, A quantum model for the stock market, Physica A 389(2010) 5769]. Our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical formalism used in the case of the quantum systems with finite-dimensional Hilbert space. The rate of return is a discrete variable corresponding to the coordinate in the case of quantum systems, and the operator of the conjugate variable describing the trend of the stock return is defined in terms of the finite Fourier transform. The stock return in equilibrium is described by a finite Gaussian function, and the time evolution of the stock price, directly related to the rate of return, is obtained by numerically solving a Schrodinger type equation.

Suggested Citation

  • Liviu-Adrian Cotfas, 2012. "A finite-dimensional quantum model for the stock market," Papers 1204.4614, arXiv.org, revised Sep 2012.
  • Handle: RePEc:arx:papers:1204.4614
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1204.4614
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, October.
    3. Pouria Pedram, 2011. "The minimal length uncertainty and the quantum model for the stock market," Papers 1111.6859, arXiv.org, revised Jan 2012.
    4. 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.
    5. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    6. Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Pouria Pedram, 2011. "The minimal length uncertainty and the quantum model for the stock market," Papers 1111.6859, arXiv.org, revised Jan 2012.
    9. 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.
    10. 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.
    11. 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.
    12. 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).
    13. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    14. Di Xiao & Jun Wang & Hongli Niu, 2016. "Volatility Analysis of Financial Agent-Based Market Dynamics from Stochastic Contact System," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 607-625, December.
    15. Jana, T.K. & Roy, P., 2011. "Supersymmetry in option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2350-2355.
    16. Liu, Haijun & Wang, Longfei, 2018. "The price momentum of stock in distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2336-2344.
    17. 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.
    18. Jaehyung Choi, 2011. "Spontaneous symmetry breaking of arbitrage," Papers 1107.5122, arXiv.org, revised Apr 2012.
    19. Jack Sarkissian, 2016. "Quantum theory of securities price formation in financial markets," Papers 1605.04948, arXiv.org, revised May 2016.
    20. Jack Sarkissian, 2016. "Spread, volatility, and volume relationship in financial markets and market making profit optimization," Papers 1606.07381, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1204.4614. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.