IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v121y2025ics0304406825000989.html

Prudence and higher-order risk attitudes in the rank-dependent utility model

Author

Listed:
  • Wang, Ruodu
  • Wu, Qinyu

Abstract

We obtain a full characterization of consistency with respect to higher-order stochastic dominance within the rank-dependent utility model. Different from the results in the literature, we do not assume any condition on the utility functions and the probability weighting functions, such as differentiability or continuity. It turns out that the level of generality that we offer leads to models that do not have a continuous probability weighting function and yet they satisfy prudence. In particular, the corresponding probability weighting function can only have a jump at 1, and must be linear on [0,1).

Suggested Citation

  • Wang, Ruodu & Wu, Qinyu, 2025. "Prudence and higher-order risk attitudes in the rank-dependent utility model," Journal of Mathematical Economics, Elsevier, vol. 121(C).
    • Handle: RePEc:eee:mateco:v:121:y:2025:i:c:s0304406825000989
    DOI: 10.1016/j.jmateco.2025.103181
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406825000989
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2025.103181?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Michèle D. Cohen, 1995. "Risk-Aversion Concepts in Expected- and Non-Expected-Utility Models," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 20(1), pages 73-91, June.
    2. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Alain Chateauneuf & Michéle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the rank-dependent expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 649-667, April.
    5. Ruodu Wang & Qinyu Wu, 2025. "The reference interval in higher-order stochastic dominance," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 263-277, October.
    6. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. 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.
    8. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    9. Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Ryan, Matthew J., 2006. "Risk aversion in RDEU," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 675-697, September.
    12. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2013. "Even (Mixed) Risk Lovers Are Prudent," American Economic Review, American Economic Association, vol. 103(4), pages 1529-1535, June.
    13. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    14. Denuit, Michel & Eeckhoudt, Louis, 2013. "Risk attitudes and the value of risk transformations," LIDAM Reprints ISBA 2013040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Alfred Müller & Marco Scarsini & Ilia Tsetlin & Robert L. Winkler, 2017. "Between First- and Second-Order Stochastic Dominance," Management Science, INFORMS, vol. 63(9), pages 2933-2947, September.
    16. Fishburn, Peter C., 1980. "Continua of stochastic dominance relations for unbounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 7(3), pages 271-285, December.
    17. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    18. Ruodu Wang & Qinyu Wu, 2024. "The reference interval in higher-order stochastic dominance," Papers 2411.15401, arXiv.org, revised Mar 2025.
    19. Eeckhoudt, Louis R. & Laeven, Roger J.A. & Schlesinger, Harris, 2020. "Risk apportionment: The dual story," Journal of Economic Theory, Elsevier, vol. 185(C).
    20. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    21. Michel M. Denuit & Louis Eeckhoudt, 2013. "Risk attitudes and the value of risk transformations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 245-254, September.
    22. Mao, Tiantian & Wang, Ruodu, 2022. "Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    23. Rachel J. Huang & Larry Y. Tzeng & Lin Zhao, 2020. "Fractional Degree Stochastic Dominance," Management Science, INFORMS, vol. 66(10), pages 4630-4647, October.
    24. Ruodu Wang & Qinyu Wu, 2025. "Probabilistic risk aversion for generalized rank-dependent functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(3), pages 1055-1082, 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. Ruodu Wang & Qinyu Wu, 2024. "Prudence and higher-order risk attitudes in the rank-dependent utility model," Papers 2412.15350, arXiv.org, revised Sep 2025.
    2. van Bruggen, Paul & Laeven, Roger J. A. & van de Kuilen, Gijs, 2024. "Higher-Order Risk Attitudes for Non-Expected Utility," Other publications TiSEM c566934e-eb60-4b4b-a972-4, Tilburg University, School of Economics and Management.
    3. Ruodu Wang & Qinyu Wu, 2024. "The reference interval in higher-order stochastic dominance," Papers 2411.15401, arXiv.org, revised Mar 2025.
    4. Louis R. Eeckhoudt & Roger J. A. Laeven, 2022. "Dual Moments and Risk Attitudes," Operations Research, INFORMS, vol. 70(3), pages 1330-1341, May.
    5. Mao, Tiantian & Wang, Ruodu, 2022. "Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    6. Louis R. Eeckhoudt & Roger J. A. Laeven, 2021. "Probability Premium and Attitude Towards Probability," Papers 2105.00054, arXiv.org.
    7. Eeckhoudt, Louis R. & Laeven, Roger J.A. & Schlesinger, Harris, 2020. "Risk apportionment: The dual story," Journal of Economic Theory, Elsevier, vol. 185(C).
    8. Sebastian Ebert & Paul Karehnke, 2025. "First-Order Prudence and Its Implications for Precautionary Savings and the Risk-Free Rate," Operations Research, INFORMS, vol. 73(6), pages 3156-3172, November.
    9. Ruodu Wang & Qinyu Wu, 2025. "The reference interval in higher-order stochastic dominance," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 263-277, October.
    10. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.
    11. Ivan Paya & David A. Peel & Konstantinos Georgalos, 2023. "On the predictions of cumulative prospect theory for third and fourth order risk preferences," Theory and Decision, Springer, vol. 95(2), pages 337-359, August.
    12. Laurie Bréban & André Lapidus, 2019. "Adam Smith on lotteries: an interpretation and formal restatement," Working Papers hal-00914222, HAL.
    13. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    14. Ryan, Matthew J., 2006. "Risk aversion in RDEU," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 675-697, September.
    15. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.
    16. Jean Baccelli, 2018. "Risk attitudes in axiomatic decision theory: a conceptual perspective," Theory and Decision, Springer, vol. 84(1), pages 61-82, January.
    17. Paan Jindapon & Liqun Liu & William S. Neilson, 2021. "Comparative risk apportionment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 91-112, April.
    18. Ivan Paya & David Peel & Konstantinos Georgalos, 2020. "On the Predictions of Cumulative Prospect Theory for Third and Fourth Order Preferences," Working Papers 293574809, Lancaster University Management School, Economics Department.
    19. Mucahit Aygun & Roger J. A. Laeven & Mitja Stadje, 2025. "Higher-Order Ambiguity Attitudes," Papers 2501.13143, arXiv.org.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:mateco:v:121:y:2025:i:c:s0304406825000989. 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.elsevier.com/locate/jmateco .

    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.