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Modeling amortization systems with vector spaces

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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.

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Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data sets used during the investigation are available from the author on reasonable request.]

Notes

  1. Finite dimensional Hilbert spaces has been widely used to model the stock market that are isomorphic to \( {\mathbb {C}} ^{d}\), where d is the discrete number of possible rates of return [44].

  2. Symmetry considerations have been explored in econophysics, where the different choice of basis of the vector space has been used to define invariant matrix rates of returns [47].

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Acknowledgements

This paper was partially supported by grants of CONICET (Argentina National Research Council) and Universidad Nacional del Sur (UNS) and by ANPCyT through PICT 2019-03491 Res. No. 015/2021 and PIP-CONICET 2021-2023 Grant No.11220200100941CO. J. S. A. is a member of CONICET.

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  1. Departamento de Física (UNS-CONICET), IFISUR, Avenida Alem 1253, Bahía Blanca, Buenos Aires, Argentina

    J. S. Ardenghi

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Ardenghi, J.S. Modeling amortization systems with vector spaces. Eur. Phys. J. B 96, 11 (2023). https://doi.org/10.1140/epjb/s10051-023-00479-1

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