IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i14p3045-3050.html
   My bibliography  Save this article

A generalization of the q-exponential discounting function

Author

Listed:
  • Cruz Rambaud, Salvador
  • Muñoz Torrecillas, María José

Abstract

The aim of this paper is to generalize the q-exponential discounting function introduced by Cajueiro (2006) [1] using the hyperbolic function as a base. The presented generalization has two aspects. First, we consider any discounting function F(t), and not just hyperbolic discounting. Second, the value of the parameter q is extended to the joint interval (−∞,1)∪(1,+∞). In this way, we have found a family of discounting functions whose elements are subadditive or superadditive according to the value of q.

Suggested Citation

  • Cruz Rambaud, Salvador & Muñoz Torrecillas, María José, 2013. "A generalization of the q-exponential discounting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3045-3050.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:14:p:3045-3050
    DOI: 10.1016/j.physa.2013.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113002124
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.03.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Takahashi, Taiki, 2008. "A comparison between Tsallis’s statistics-based and generalized quasi-hyperbolic discount models in humans," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 551-556.
    2. Han, Ruokang & Takahashi, Taiki, 2012. "Psychophysics of time perception and valuation in temporal discounting of gain and loss," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6568-6576.
    3. Cajueiro, Daniel O., 2006. "A note on the relevance of the q-exponential function in the context of intertemporal choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 385-388.
    4. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    5. McAlvanah, Patrick, 2010. "Subadditivity, patience, and utility: The effects of dividing time intervals," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 325-337, November.
    6. Takahashi, Taiki, 2007. "A comparison of intertemporal choices for oneself versus someone else based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 637-644.
    7. Read, Daniel, 2001. "Is Time-Discounting Hyperbolic or Subadditive?," Journal of Risk and Uncertainty, Springer, vol. 23(1), pages 5-32, July.
    8. Marc Scholten & Daniel Read, 2006. "Discounting by Intervals: A Generalized Model of Intertemporal Choice," Management Science, INFORMS, vol. 52(9), pages 1424-1436, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lu, Yang & Zhuang, Xintian, 2014. "The impact of gender and working experience on intertemporal choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 146-153.
    2. 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.
    3. Lu, Yang & Wu, Dongmei & Zhuang, Xintian, 2016. "Part-whole bias in intertemporal choice: An empirical study of additive assumption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 231-235.
    4. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    5. 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.
    6. Salvador Cruz Rambaud & Isabel González Fernández & Viviana Ventre, 2018. "Modeling the inconsistency in intertemporal choice: the generalized Weibull discount function and its extension," Annals of Finance, Springer, vol. 14(3), pages 415-426, August.

    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. Lu, Yang & Wu, Dongmei & Zhuang, Xintian, 2016. "Part-whole bias in intertemporal choice: An empirical study of additive assumption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 231-235.
    2. Destefano, Natália & Martinez, Alexandre Souto, 2011. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1763-1772.
    3. 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.
    4. dos Santos, Lindomar Soares & Destefano, Natália & Martinez, Alexandre Souto, 2018. "Decision making generalized by a cumulative probability weighting function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 250-259.
    5. Natalia Destefano & Alexandre Souto Martinez, 2010. "The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws," Papers 1010.5648, arXiv.org, revised May 2011.
    6. 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.
    7. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    8. Alexandre Souto Martinez & Rodrigo Silva Gonzalez & Cesar Augusto Sangaletti Tercariol, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Papers 0803.2635, arXiv.org, revised May 2008.
    9. Lu, Yang & Zhuang, Xintian, 2014. "The impact of gender and working experience on intertemporal choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 146-153.
    10. Takahashi, Taiki & Oono, Hidemi & Radford, Mark H.B., 2008. "Psychophysics of time perception and intertemporal choice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2066-2074.
    11. Shou Chen & Richard Fu & Lei Wedge & Ziran Zou, 2019. "Non-hyperbolic discounting and dynamic preference reversal," Theory and Decision, Springer, vol. 86(2), pages 283-302, March.
    12. Salvador Cruz Rambaud & Isabel González Fernández & Viviana Ventre, 2018. "Modeling the inconsistency in intertemporal choice: the generalized Weibull discount function and its extension," Annals of Finance, Springer, vol. 14(3), pages 415-426, August.
    13. Takahashi, Taiki, 2010. "A social discounting model based on Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3600-3603.
    14. Uri Ben-Zion & Jan Pieter Krahnen & TAL SHAVIT, 2007. "Subjective Evaluation Of Delayed Risky Outcomes: An Experimental Approach," Working Papers 0709, Ben-Gurion University of the Negev, Department of Economics.
    15. Alekseev, Aleksandr & Sokolov, Mikhail V., 2021. "How to measure the average rate of change?," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 43-59.
    16. Andrew Meyer, 2013. "Estimating discount factors for public and private goods and testing competing discounting hypotheses," Journal of Risk and Uncertainty, Springer, vol. 46(2), pages 133-173, April.
    17. repec:cup:judgdm:v:8:y:2013:i:2:p:116-135 is not listed on IDEAS
    18. Wang, Mei & Rieger, Marc Oliver & Hens, Thorsten, 2016. "How time preferences differ: Evidence from 53 countries," Journal of Economic Psychology, Elsevier, vol. 52(C), pages 115-135.
    19. Mohammed Abdellaoui & Han Bleichrodt & Olivier l’Haridon, 2013. "Sign-dependence in intertemporal choice," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 225-253, December.
    20. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    21. Marc Scholten & Daniel Read, 2006. "Discounting by Intervals: A Generalized Model of Intertemporal Choice," Management Science, INFORMS, vol. 52(9), pages 1424-1436, September.
    22. Jos'e Cl'audio do Nascimento, 2019. "Rational hyperbolic discounting," Papers 1910.05209, arXiv.org, revised Feb 2020.

    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:eee:phsmap:v:392:y:2013:i:14:p:3045-3050. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.