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An Extension of the Concept of Derivative: Its Application to Intertemporal Choice

Author

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  • Salvador Cruz Rambaud

    (Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain)

  • Blas Torrecillas Jover

    (Departamento de Matemáticas, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain)

Abstract

The framework of this paper is the concept of derivative from the point of view of abstract algebra and differential calculus. The objective of this paper is to introduce a novel concept of derivative which arises in certain economic problems, specifically in intertemporal choice when trying to characterize moderately and strongly decreasing impatience. To do this, we have employed the usual tools and magnitudes of financial mathematics with an algebraic nomenclature. The main contribution of this paper is twofold. On the one hand, we have proposed a novel framework and a different approach to the concept of relative derivation which satisfies the so-called generalized Leibniz’s rule. On the other hand, in spite of the fact that this peculiar approach can be applied to other disciplines, we have presented the mathematical characterization of the two main types of decreasing impatience in the ambit of behavioral finance, based on a previous characterization involving the proportional increasing of the variable “time”. Finally, this paper points out other patterns of variation which could be applied in economics and other scientific disciplines.

Suggested Citation

  • Salvador Cruz Rambaud & Blas Torrecillas Jover, 2020. "An Extension of the Concept of Derivative: Its Application to Intertemporal Choice," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:696-:d:353209
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    References listed on IDEAS

    as
    1. Nina Anchugina & Matthew Ryan & Arkadii Slinko, 2016. "Aggregating time preferences with decreasing impatience," Papers 1604.01819, arXiv.org.
    2. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(1), pages 109-126, March.
    3. Manel Baucells & Franz H. Heukamp, 2012. "Probability and Time Trade-Off," Management Science, INFORMS, vol. 58(4), pages 831-842, April.
    4. Salvador Cruz Rambaud & María José Muñoz Torrecillas, 2016. "Measuring Impatience in Intertemporal Choice," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-17, February.
    5. Vijay Gupta & Themistocles M. Rassias & P. N. Agrawal & Ana Maria Acu, 2018. "Basics of Post-quantum Calculus," Springer Optimization and Its Applications, in: Recent Advances in Constructive Approximation Theory, chapter 0, pages 73-89, Springer.
    6. Vijay Gupta & Themistocles M. Rassias & P. N. Agrawal & Ana Maria Acu, 2018. "Recent Advances in Constructive Approximation Theory," Springer Optimization and Its Applications, Springer, number 978-3-319-92165-5, September.
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