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Open AccessArticle

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

1
Departamento de Economía y Empresa, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain
2
Departamento de Matemáticas, Universidad de Almería, La Cañada de San Urbano, s/n, 04120 Almería, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 696; https://doi.org/10.3390/math8050696
Received: 26 March 2020 / Revised: 25 April 2020 / Accepted: 26 April 2020 / Published: 2 May 2020
(This article belongs to the Special Issue Quantitative Methods for Economics and Finance)
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. View Full-Text
Keywords: derivation; intertemporal choice; decreasing impatience; elasticity derivation; intertemporal choice; decreasing impatience; elasticity
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Cruz Rambaud, S.; Torrecillas Jover, B. An Extension of the Concept of Derivative: Its Application to Intertemporal Choice. Mathematics 2020, 8, 696.

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