IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v567y2021ics0378437120309547.html
   My bibliography  Save this article

Quantum credit loans

Author

Listed:
  • Ardenghi, J.S.

Abstract

Quantum models based on the mathematics of quantum mechanics (QM) have been developed in cognitive sciences, game theory and econophysics. In this work a generalization of credit loans is introduced by using the vector space formalism of QM. Operators for the debt, amortization, interest and periodic installments are defined and its mean values in an arbitrary orthonormal basis of the vectorial space give the corresponding values at each period of the loan. Endowing the vector space of dimension M, where M is the loan duration, with a SO(M) symmetry, it is possible to rotate the eigenbasis to obtain better schedule periodic payments for the borrower, by using the rotation angles of the SO(M) transformation. Given that a rotation preserves the length of the vectors, the total amortization, debt and periodic installments are not changed. For a general description of the formalism introduced, the loan operator relations are given in terms of a generalized Heisenberg algebra, where finite dimensional representations are considered and commutative operators are defined for the specific loan types. The results obtained are an improvement of the usual financial instrument of credit because introduce several degrees of freedom through the rotation angles, which allows to select superposition states of the corresponding commutative operators that enables the borrower to tune the periodic installments in order to obtain better benefits without changing what the lender earns.

Suggested Citation

  • Ardenghi, J.S., 2021. "Quantum credit loans," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    • Handle: RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120309547
    DOI: 10.1016/j.physa.2020.125656
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120309547
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.125656?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
    2. Choustova, Olga Al., 2007. "Quantum Bohmian model for financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 304-314.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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).
    4. 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.
    5. Liviu-Adrian Cotfas & Camelia Delcea & Nicolae Cotfas, 2014. "Exact solution of a generalized version of the Black-Scholes equation," Papers 1411.2628, arXiv.org.
    6. 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.
    7. F. Bagarello & E. Haven, 2014. "Towards a formalization of a two traders market with information exchange," Papers 1412.8725, arXiv.org.
    8. 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.
    9. 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.
    10. Bagarello, F., 2011. "Damping in quantum love affairs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2803-2811.
    11. 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.
    12. Paras M. Agrawal & Ramesh Sharda, 2013. "OR Forum---Quantum Mechanics and Human Decision Making," Operations Research, INFORMS, vol. 61(1), pages 1-16, February.
    13. 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.
    14. 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).
    15. 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.
    16. Ashtiani, Mehrdad & Azgomi, Mohammad Abdollahi, 2015. "A survey of quantum-like approaches to decision making and cognition," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 49-80.
    17. Raymond J. Hawkins & B. Roy Frieden, 2012. "Asymmetric Information and Quantization in Financial Economics," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, December.
    18. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    19. Khrennikova, Polina, 2016. "Application of quantum master equation for long-term prognosis of asset-prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 253-263.
    20. Anantya Bhatnagar & Dimitri D. Vvedensky, 2022. "Quantum effects in an expanded Black–Scholes model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(8), pages 1-12, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120309547. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.