IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2403.15319.html
   My bibliography  Save this paper

Discounted Subjective Expected Utility in Continuous Time

Author

Listed:
  • Lorenzo Bastianello
  • Vassili Vergopoulos

Abstract

By embedding uncertainty into time, we obtain a conjoint axiomatic characterization of both Exponential Discounting and Subjective Expected Utility that accommodates arbitrary state and outcome spaces. In doing so, we provide a novel and simple time-interpretation of subjective probability. The subjective probability of an event is calibrated using time discounting.

Suggested Citation

  • Lorenzo Bastianello & Vassili Vergopoulos, 2024. "Discounted Subjective Expected Utility in Continuous Time," Papers 2403.15319, arXiv.org.
    • Handle: RePEc:arx:papers:2403.15319
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2403.15319
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    2. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    3. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    4. Howard Raiffa, 1961. "Risk, Ambiguity, and the Savage Axioms: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 690-694.
    5. Ghirardato, Paolo & Pennesi, Daniele, 2020. "A general theory of subjective mixtures," Journal of Economic Theory, Elsevier, vol. 188(C).
    6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    7. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    8. Marcus Pivato, 2021. "Intertemporal Choice with Continuity Constraints," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1203-1229, August.
    9. Harvey, Charles M. & Østerdal, Lars Peter, 2012. "Discounting models for outcomes over continuous time," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 284-294.
    10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    11. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    12. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    13. Asen Kochov, 2015. "Time and No Lotteries: An Axiomatization of Maxmin Expected Utility," Econometrica, Econometric Society, vol. 83, pages 239-262, January.
    14. Hara, Kazuhiro, 2016. "Characterization of stationary preferences in a continuous time framework," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 34-43.
    15. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    16. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
    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. Michel Grabisch & Benjamin Monet & Vassili Vergopoulos, 2023. "Subjective expected utility through stochastic independence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 723-757, October.
    2. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    3. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    4. Jürgen Eichberger & Simon Grant & David Kelsey, 2016. "Randomization and dynamic consistency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(3), pages 547-566, August.
    5. Paolo Ghirardato & Daniele Pennesi, 2023. "Randomizing without randomness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 1009-1037, May.
    6. Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.
    7. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    8. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    9. Ilke Aydogan & Loic Berger & Valentina Bosetti & Ning Liu, 2018. "Three layers of uncertainty: an experiment," Working Papers 623, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    10. Xiangyu Qu, 2015. "A belief-based definition of ambiguity aversion," Theory and Decision, Springer, vol. 79(1), pages 15-30, July.
    11. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    12. Bleichrodt, Han & Eichberger, Jürgen & Grant, Simon & Kelsey, David & Li, Chen, 2021. "Testing dynamic consistency and consequentialism under ambiguity," European Economic Review, Elsevier, vol. 134(C).
    13. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
    14. Han Bleichrodt & Jurgen Eichberger & Simon Grant & David Kelsey & Chen Li, 2018. "A Test of Dynamic Consistency and Consequentialism in the Presence of Ambiguity," Discussion Papers 1803, University of Exeter, Department of Economics.
    15. Qu, Xiangyu, 2013. "Maxmin expected utility with additivity on unambiguous events," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 245-249.
    16. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    17. Christoph Bühren & Fabian Meier & Marco Pleßner, 2023. "Ambiguity aversion: bibliometric analysis and literature review of the last 60 years," Management Review Quarterly, Springer, vol. 73(2), pages 495-525, June.
    18. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    19. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
    20. Ralf Diedrich, 2024. "Combining Savage and Laplace: a new approach to ambiguity," Theory and Decision, Springer, vol. 97(3), pages 423-453, November.

    More about this item

    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:arx:papers:2403.15319. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.