IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v126y2026ics0167668725001258.html

Zero utility principle under uncertainty

Author

Listed:
  • Chudziak, J.
  • Wójcik, S.

Abstract

We introduce and investigate the zero utility principle in the Cumulative Prospect Theory under uncertainty. We prove the existence of the principle and characterize its important properties (comparability, equality, positive homogeneity, comonotonic additivity, and subadditivity). Moreover, we show that the zero utility principle under uncertainty can be uniquely extended from the family of binary risks onto the family of all risks.

Suggested Citation

  • Chudziak, J. & Wójcik, S., 2026. "Zero utility principle under uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 126(C).
    • Handle: RePEc:eee:insuma:v:126:y:2026:i:c:s0167668725001258
    DOI: 10.1016/j.insmatheco.2025.103178
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668725001258
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2025.103178?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. Marek Kuczma, 2009. "An Introduction to the Theory of Functional Equations and Inequalities," Springer Books, Springer, edition 0, number 978-3-7643-8749-5 edited by Attila Gilányi, January.
    2. Tiantian Mao & Jun Cai, 2018. "Risk measures based on behavioural economics theory," Finance and Stochastics, Springer, vol. 22(2), pages 367-393, April.
    3. 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.
    4. Sainan Zhang & Huifu Xu, 2022. "Insurance premium-based shortfall risk measure induced by cumulative prospect theory," Computational Management Science, Springer, vol. 19(4), pages 703-738, October.
    5. Chudziak, J., 2020. "On positive homogeneity and comonotonic additivity of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 154-159.
    6. Heilpern, S., 2003. "A rank-dependent generalization of zero utility principle," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 67-73, August.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    8. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 159-166.
    9. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "A note on additive risk measures in rank-dependent utility," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 187-189, October.
    10. Chudziak, J., 2018. "On existence and uniqueness of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 243-246.
    11. Kaluszka, Marek & Krzeszowiec, Michał, 2013. "On iterative premium calculation principles under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 435-440.
    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. Martina Nardon & Paolo Pianca, 2019. "Behavioral premium principles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 229-257, June.
    2. Chudziak, J., 2020. "On positive homogeneity and comonotonic additivity of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 154-159.
    3. Martina Nardon & Paolo Pianca, 2019. "Insurance premium calculation under continuous cumulative prospect theory," Working Papers 2019:03, Department of Economics, University of Venice "Ca' Foscari".
    4. Marek Kałuszka & Michał Krzeszowiec, 2013. "Iteracyjność składek ubezpieczeniowych w ujęciu teorii skumulowanej perspektywy i teorii nieokreśloności," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 45-56.
    5. Sainan Zhang & Huifu Xu, 2022. "Insurance premium-based shortfall risk measure induced by cumulative prospect theory," Computational Management Science, Springer, vol. 19(4), pages 703-738, October.
    6. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    7. Kaluszka, Marek & Krzeszowiec, Michał, 2013. "On iterative premium calculation principles under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 435-440.
    8. Chudziak, J., 2018. "On existence and uniqueness of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 243-246.
    9. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 159-166.
    10. Choo, Weihao & de Jong, Piet, 2015. "The tradeoff insurance premium as a two-sided generalisation of the distortion premium," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 238-246.
    11. Zhenfeng Zou, 2026. "Generalized Optimal Initial Capital and Risk Measures Induced by the Generalized Certainty Equivalent," Methodology and Computing in Applied Probability, Springer, vol. 28(1), pages 1-24, March.
    12. Kaluszka, M. & Laeven, R.J.A. & Okolewski, A., 2012. "A note on weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 379-381.
    13. Mao, Tiantian & Stupfler, Gilles & Yang, Fan, 2023. "Asymptotic properties of generalized shortfall risk measures for heavy-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 173-192.
    14. De Vecchi, Corrado & Scherer, Matthias, 2025. "Pricing insurance contracts with an existing portfolio as background risk," Insurance: Mathematics and Economics, Elsevier, vol. 122(C), pages 180-193.
    15. Joanna Dębicka & Stanisław Heilpern, 2020. "The optimization of insurance contracts on the viatical market," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(2), pages 5-27.
    16. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "A note on additive risk measures in rank-dependent utility," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 187-189, October.
    17. Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.
    18. Tiantian Mao & Jun Cai, 2018. "Risk measures based on behavioural economics theory," Finance and Stochastics, Springer, vol. 22(2), pages 367-393, April.
    19. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    20. Roberto Cominetti & Alfredo Torrico, 2016. "Additive Consistency of Risk Measures and Its Application to Risk-Averse Routing in Networks," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1510-1521, November.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:insuma:v:126:y:2026:i:c:s0167668725001258. 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/inca/505554 .

    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.