IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03256606.html
   My bibliography  Save this paper

From Decision in Risk to Decision in Time - and Return: A Restatement of Probability Discounting

Author

Listed:
  • Marc-Arthur Diaye

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • André Lapidus

    (PHARE - Philosophie, Histoire et Analyse des Représentations Économiques - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Christian Schmidt

    (PHARE - Philosophie, Histoire et Analyse des Représentations Économiques - UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

This paper aims to restate, in a decision theory framework, the results of some significant contributions of the literature on probability discounting that followed the publication of the pioneering article by Rachlin et al. We provide a restatement of probability discounting, usually limited to the case of 2-issues lotteries, in terms of rank-dependent utility, in which the utilities of the outcomes of n-issues lotteries are weighted by probabilities transformed after their transposition into time-delays. This formalism makes the typical cases of rationality in time and in risk mutually exclusive, but allows looser types of rationality. The resulting attitude toward probability and toward risk are then determined in relation to the values of the two parameters involved in the procedure of probability discounting: a parameter related to impatience and pessimism, and a parameter related to time-consistency and the separation between non-optimism and non-pessimism. A simulation illustrates these results through the characteristics of the transformation of probabilities function.

Suggested Citation

  • Marc-Arthur Diaye & André Lapidus & Christian Schmidt, 2024. "From Decision in Risk to Decision in Time - and Return: A Restatement of Probability Discounting," Post-Print hal-03256606, HAL.
    • Handle: RePEc:hal:journl:hal-03256606
    DOI: 10.4236/tel.2024.145101
    Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03256606v2
    as

    Download full text from publisher

    File URL: https://paris1.hal.science/hal-03256606v2/document
    Download Restriction: no
    File URL: https://libkey.io/10.4236/tel.2024.145101?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
    ---><---

    References listed on IDEAS

    as
    1. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    2. María José Muñoz Torrecillas & Taiki Takahashi & Jesús Gil Roales-Nieto & Salvador Cruz Rambaud & Zaida Callejón Ruiz & Blas Torrecillas Jover, 2018. "Impatience and Inconsistency in Intertemporal Choice: An Experimental Analysis," Journal of Behavioral Finance, Taylor & Francis Journals, vol. 19(2), pages 190-198, April.
    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. Marc-Arthur Diaye & André Lapidus & Christian Schmidt, 2024. "From Decision in Risk to Decision in Time - and Return: A Restatement of Probability Discounting," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03256606, HAL.
    2. repec:hal:wpaper:hal-03256606 is not listed on IDEAS
    3. repec:dau:papers:123456789/2348 is not listed on IDEAS
    4. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, vol. 119(1), pages 35-49, November.
    5. Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
    6. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    7. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    8. George Georgiadis & Doron Ravid & Balázs Szentes, 2024. "Flexible Moral Hazard Problems," Econometrica, Econometric Society, vol. 92(2), pages 387-409, March.
    9. Strzalecki, Tomasz & Werner, Jan, 2011. "Efficient allocations under ambiguity," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1173-1194, May.
    10. Michèle Cohen, 2008. "Risk Perception, Risk Attitude and Decision : a Rank-Dependent Approach," Post-Print halshs-00348810, HAL.
    11. Grant, S. & Quiggin, J., 2001. "A Model-Free Definition of Increasing Uncertainty," Discussion Paper 2001-84, Tilburg University, Center for Economic Research.
    12. Assa, Hirbod & Zimper, Alexander, 2018. "Preferences over all random variables: Incompatibility of convexity and continuity," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 71-83.
    13. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
    14. Arthur Charpentier & Alfred Galichon & Marc Henry, 2012. "Local Utility and Multivariate Risk Aversion," CIRJE F-Series CIRJE-F-836, CIRJE, Faculty of Economics, University of Tokyo.
    15. Quiggin, John & Chambers, Robert G., 2006. "Supermodularity and risk aversion," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 1-14, July.
    16. Alain Chateauneuf & Ghizlane Lakhnati & Eric Langlais, 2016. "On the precautionary motive for savings and prudence in the rank-dependent utility framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 169-182, January.
    17. Servaas van Bilsen & Roger J. A. Laeven & Theo E. Nijman, 2020. "Consumption and Portfolio Choice Under Loss Aversion and Endogenous Updating of the Reference Level," Management Science, INFORMS, vol. 66(9), pages 3927-3955, September.
    18. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    19. Albrecht, Peter & Huggenberger, Markus, 2017. "The fundamental theorem of mutual insurance," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 180-188.
    20. Matthew D. Rablen, 2023. "Loss Aversion, Risk Aversion, and the Shape of the Probability Weighting Function," Working Papers 2023013, The University of Sheffield, Department of Economics.
    21. Trabelsi, Mohamed Ali, 2006. "Les nouveaux modèles de décision dans le risque et l’incertain : quel apport ? [The new models of decision under risk or uncertainty : What approach?]," MPRA Paper 25442, University Library of Munich, Germany.
    22. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1998. "Intrinsic Preference for Information," Journal of Economic Theory, Elsevier, vol. 83(2), pages 233-259, December.

    More about this item

    Keywords

    Probability discounting; Time discounting; Logarithmic time perception; Rank-dependent utility; Rationality; Attitude toward probabilities; Attitude toward risk;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:hal:journl:hal-03256606. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.