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A generalization of the q-exponential discounting function

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    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. 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.
    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. 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.
    5. 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.
    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.

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