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Stock markets and quantum dynamics: A second quantized description

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  • Bagarello, F.

Abstract

In this paper we continue our description of stock markets in terms of some non-abelian operators which are used to describe the portfolio of the various traders and other observable quantities. After a first prototype model with only two traders, we discuss a more realistic model of market involving an arbitrary number of traders. For both models we find approximated solutions for the time evolution of the portfolio of each trader. In particular, for the more realistic model, we use the stochastic limit approach and a fixed point like approximation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:283-302
    DOI: 10.1016/j.physa.2007.08.031
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Ana Njegovanović, 2023. "The Importance of Quantum Information in the Stock Market and Financial Decision Making in Conditions of Radical Uncertainty," International Journal of Social Science Studies, Redfame publishing, vol. 11(1), pages 54-71, January.
    4. Bagarello, F. & Haven, E., 2014. "The role of information in a two-traders market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 224-233.
    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. Jasmina Jekni'c-Dugi'c & Sonja Radi' c & Igor Petrovi'c & Momir Arsenijevi'c & Miroljub Dugi'c, 2018. "Quantum Brownian oscillator for the stock market," Papers 1901.10544, arXiv.org.
    8. F. Bagarello & E. Haven, 2014. "Towards a formalization of a two traders market with information exchange," Papers 1412.8725, arXiv.org.
    9. Bagarello, F., 2011. "Damping in quantum love affairs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2803-2811.

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