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Modeling amortization systems with vector spaces

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  • J. S. Ardenghi

    (IFISUR)

Abstract

Amortization systems are used widely in economy to generate payment schedules to repaid an initial debt with its interest. We present a generalization of these amortization systems by introducing the mathematical formalism of quantum mechanics based on vector spaces. Operators are defined for debt, amortization, interest and periodic payment and their mean values are computed in different orthonormal basis. The vector space of the amortization system will have dimension M, where M is the loan maturity and the vectors will have a SO(M) symmetry, yielding the possibility of rotating the basis of the vector space while preserving the distance among vectors. The results obtained are useful to add degrees of freedom to the usual amortization systems without affecting the interest profits of the lender while also benefitting the borrower who is able to alter the payment schedules. Furthermore, using the tensor product of algebras, we introduce loans entanglement in which two borrowers can correlate the payment schedules without altering the total repaid. Graphical abstract

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  • 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.
    • Handle: RePEc:spr:eurphb:v:96:y:2023:i:1:d:10.1140_epjb_s10051-023-00479-1
    DOI: 10.1140/epjb/s10051-023-00479-1
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    References listed on IDEAS

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    1. Choustova, Olga Al., 2007. "Quantum Bohmian model for financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 304-314.
    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. Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
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