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A quantum statistical approach to simplified stock markets

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  • Fabio Bagarello

Abstract

We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the {\em portfolio} of a certain trader to a different one. This computation can also be carried out using some kind of {\em Feynman graphs} adapted to the present context.

Suggested Citation

  • Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
    • Handle: RePEc:arx:papers:0907.2531
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    Cited by:

    1. 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.
    2. F. Bagarello & E. Haven, 2014. "Towards a formalization of a two traders market with information exchange," Papers 1412.8725, arXiv.org.
    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. Kuzu, Erkan & Süsay, Aynur & Tanrıöven, Cihan, 2022. "A model study for calculation of the temperatures of major stock markets in the world with the quantum simulation and determination of the crisis periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    5. J. S. Ardenghi, 2023. "Modeling amortization systems with vector spaces," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-12, January.
    6. Bagarello, F., 2011. "Damping in quantum love affairs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2803-2811.
    7. 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.
    8. Kumar, Sushil & Kumar, Sunil & Kumar, Pawan, 2020. "Diffusion entropy analysis and random matrix analysis of the Indian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    9. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    10. Ardenghi, J.S., 2021. "Quantum credit loans," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    11. Liviu-Adrian Cotfas & Camelia Delcea & Nicolae Cotfas, 2014. "Exact solution of a generalized version of the Black-Scholes equation," Papers 1411.2628, arXiv.org.
    12. 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.
    13. 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.
    14. Pineiro-Chousa, Juan & Vizcaíno-González, Marcos, 2016. "A quantum derivation of a reputational risk premium," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 304-309.
    15. Paras M. Agrawal & Ramesh Sharda, 2013. "OR Forum---Quantum Mechanics and Human Decision Making," Operations Research, INFORMS, vol. 61(1), pages 1-16, February.
    16. 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.
    17. Meng, Xiangyi & Zhang, Jian-Wei & Guo, Hong, 2016. "Quantum Brownian motion model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 281-288.

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