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The minimal length uncertainty and the quantum model for the stock market

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  • Pedram, Pouria
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    Abstract

    We generalize the recently proposed quantum model for the stock market by Zhang and Huang to make it consistent with the discrete nature of the stock price. In this formalism, the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized Hamiltonian contains an additional term proportional to the fourth power of the trend. We study a driven infinite quantum well where information as the external field periodically fluctuates and show that the presence of the minimal trading value of stocks results in a positive shift in the characteristic frequencies of the quantum system. The connection between the information frequency and the transition probabilities is discussed finally.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111008788
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    Bibliographic Info

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

    Volume (Year): 391 (2012)
    Issue (Month): 5 ()
    Pages: 2100-2105

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    Handle: RePEc:eee:phsmap:v:391:y:2012:i:5:p:2100-2105

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

    Related research

    Keywords: Econophysics; Quantum finance; Generalized uncertainty relation; Minimal length;

    References

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    1. Ye, C. & Huang, J.P., 2008. "Non-classical oscillator model for persistent fluctuations in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1255-1263.
    2. 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.
    3. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    4. F. Bagarello, 2009. "Simplified stock markets described by number operators," Papers 0904.3213, arXiv.org.
    5. Martin Schaden, 2002. "Quantum Finance," Papers physics/0203006, arXiv.org, revised Aug 2002.
    6. Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
    7. Schaden, Martin, 2002. "Quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 511-538.
    8. 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.
    9. Ataullah, Ali & Davidson, Ian & Tippett, Mark, 2009. "A wave function for stock market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 455-461.
    10. Fabio Bagarello, 2007. "The Heisenberg picture in the analysis of stock markets and in other sociological contexts," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(4), pages 533-544, August.
    11. Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    13. Bagarello, F., 2007. "Stock markets and quantum dynamics: A second quantized description," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 283-302.
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    Cited by:
    1. 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.
    2. Liviu-Adrian Cotfas, 2012. "A finite-dimensional quantum model for the stock market," Papers 1204.4614, arXiv.org, revised Sep 2012.
    3. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.

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