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A finite-dimensional quantum model for the stock market

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  • Cotfas, Liviu-Adrian
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    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 Schrödinger type equation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 392 (2013)
    Issue (Month): 2 ()
    Pages: 371-380

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    Handle: RePEc:eee:phsmap:v:392:y:2013:i:2:p:371-380

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Econophysics; Quantum finance; Finite quantum systems;

    References

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    1. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    2. Choustova, Olga Al., 2007. "Quantum Bohmian model for financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 304-314.
    3. 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.
    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. 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.
    6. Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
    7. Bagarello, F., 2009. "A quantum statistical approach to simplified stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4397-4406.
    8. Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
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    Cited by:
    1. 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.

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