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A quantum model for the stock market

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  • Zhang, Chao
  • Huang, Lu
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    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.

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    Bibliographic Info

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

    Volume (Year): 389 (2010)
    Issue (Month): 24 ()
    Pages: 5769-5775

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    Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5769-5775

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

    Related research

    Keywords: Econophysics; Quantum finance; Stock market; Quantum model; Stock price; Rate of return;

    References

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    1. Piotrowski, Edward W. & Sładkowski, Jan, 2005. "Quantum diffusion of prices and profits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 185-195.
    2. Fabio Bagarello, 2007. "The Heisenberg picture in the analysis of stock markets and in other sociological contexts," Quality & Quantity: International Journal of Methodology, Springer, Springer, vol. 41(4), pages 533-544, August.
    3. Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
    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. 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.
    6. 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.
    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.
    8. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    9. Schaden, Martin, 2002. "Quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 511-538.
    10. 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.
    11. Martin Schaden, 2002. "Quantum Finance," Papers physics/0203006, arXiv.org, revised Aug 2002.
    12. F. Bagarello, 2009. "Simplified stock markets described by number operators," Papers 0904.3213, arXiv.org.
    13. Linden, Mikael, 2005. "Estimating the distribution of volatility of realized stock returns and exchange rate changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 573-583.
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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.
    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. Liviu-Adrian Cotfas, 2012. "Finite quantum mechanical model for the stock market," Papers 1208.6146, arXiv.org, revised Sep 2012.
    4. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    5. 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.
    6. Pouria Pedram, 2011. "The minimal length uncertainty and the quantum model for the stock market," Papers 1111.6859, arXiv.org, revised Jan 2012.
    7. Liviu-Adrian Cotfas, 2012. "A finite-dimensional quantum model for the stock market," Papers 1204.4614, arXiv.org, revised Sep 2012.

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