IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p696-d353209.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/696/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/696/
    Download Restriction: no
    ---><---

    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, June.
    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. Cruz Rambaud, Salvador & Parra Oller, Isabel María & Valls Martínez, María del Carmen, 2018. "The amount-based deformation of the q-exponential discount function: A joint analysis of delay and magnitude effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 788-796.
    2. Salvador Cruz Rambaud & Isabel González Fernández, 2019. "A measure of inconsistencies in intertemporal choice," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-24, October.
    3. Sun, Yuxin & Ibikunle, Gbenga, 2017. "Informed trading and the price impact of block trades: A high frequency trading analysis," International Review of Financial Analysis, Elsevier, vol. 54(C), pages 114-129.
    4. Fischer, Andreas M. & Ranaldo, Angelo, 2011. "Does FOMC news increase global FX trading?," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2965-2973, November.
    5. Mende, Alexander, 2005. "09/11 on the USD/EUR Foreign Exchange Market," Hannover Economic Papers (HEP) dp-312, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. Ana Maria Acu & Sever Hodiş & Ioan Rașa, 2020. "Estimates for the Differences of Certain Positive Linear Operators," Mathematics, MDPI, vol. 8(5), pages 1-12, May.
    7. Chan, Kalok & Covrig, Vicentiu, 2012. "What determines mutual fund trading in foreign stocks?," Journal of International Money and Finance, Elsevier, vol. 31(4), pages 793-817.
    8. Koski, Jennifer Lynch, 1998. "Measurement Effects and the Variance of Returns after Stock Splits and Stock Dividends," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 143-162.
    9. Konishi, Hizuru, 2002. "Optimal slice of a VWAP trade," Journal of Financial Markets, Elsevier, vol. 5(2), pages 197-221, April.
    10. Michelle B Graczyk & Sílvio M Duarte Queirós, 2017. "Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-23, July.
    11. Sabbaghi, Omid & Sabbaghi, Navid, 2011. "Carbon Financial Instruments, thin trading, and volatility: Evidence from the Chicago Climate Exchange," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(4), pages 399-407.
    12. Do, Hung Xuan & Brooks, Robert & Treepongkaruna, Sirimon & Wu, Eliza, 2014. "How does trading volume affect financial return distributions?," International Review of Financial Analysis, Elsevier, vol. 35(C), pages 190-206.
    13. Brockman, Paul & Chung, Dennis Y., 2000. "An empirical investigation of trading on asymmetric information and heterogeneous prior beliefs," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 417-454, December.
    14. Gagnon, Louis & Karolyi, G. Andrew, 2009. "Information, Trading Volume, and International Stock Return Comovements: Evidence from Cross-Listed Stocks," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(4), pages 953-986, August.
    15. Abhinava Tripathi, 2021. "The Arrival of Information and Price Adjustment Across Extreme Quantiles: Global Evidence," IIM Kozhikode Society & Management Review, , vol. 10(1), pages 7-19, January.
    16. repec:dau:papers:123456789/11681 is not listed on IDEAS
    17. Van Geyt, Debby & Van Cauwenberge, Philippe & Vander Bauwhede, Heidi, 2014. "Does high-quality corporate communication reduce insider trading profitability?," International Review of Law and Economics, Elsevier, vol. 37(C), pages 1-14.
    18. Flannery, Mark J. & Kwan, Simon H. & Nimalendran, Mahendrarajah, 2013. "The 2007–2009 financial crisis and bank opaqueness," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 55-84.
    19. Kenneth Yung & Yen-Chih Liu, 2009. "Implications of futures trading volume: Hedgers versus speculators," Journal of Asset Management, Palgrave Macmillan, vol. 10(5), pages 318-337, December.
    20. Lo, Keng-Hsin & Wang, Kehluh & Liao, Tsai-Ling, 2006. "Insider transfer trading of banking companies around exchange listing," Journal of Financial Intermediation, Elsevier, vol. 15(2), pages 215-234, April.
    21. Carsten Detken & Philipp Hartmann, 2000. "The Euro and International Capital Markets," International Finance, Wiley Blackwell, vol. 3(1), pages 53-94, April.

    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:gam:jmathe:v:8:y:2020:i:5:p:696-:d:353209. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.