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

  • Pouria Pedram
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    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://arxiv.org/pdf/1111.6859
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    Paper provided by arXiv.org in its series Papers with number 1111.6859.

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    Date of creation: Nov 2011
    Date of revision: Jan 2012
    Publication status: Published in Physica A 391, 2100 (2012)
    Handle: RePEc:arx:papers:1111.6859
    Contact details of provider: Web page: http://arxiv.org/

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    1. 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.
    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. 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.
    4. 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.
    5. Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
    6. 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.
    7. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    8. 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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