The minimal length uncertainty and the quantum model for the stock market
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 391 (2012)
Issue (Month): 5 ()
|Contact details of provider:|| Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
- Martin Schaden, 2002. "Quantum Finance," Papers physics/0203006, arXiv.org, revised Aug 2002.
- 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.
- 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.
- Schaden, Martin, 2002. "Quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 511-538.
- 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.
- 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.
- F. Bagarello, 2009. "Simplified stock markets described by number operators," Papers 0904.3213, arXiv.org.
- 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.
- 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.
- Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
- Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:5:p:2100-2105. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.