IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v104y2015icp22-25.html
   My bibliography  Save this article

A simple proof for the convexity of the Choquet integral

Author

Listed:
  • Alfonsi, Aurélien

Abstract

This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.

Suggested Citation

  • Alfonsi, Aurélien, 2015. "A simple proof for the convexity of the Choquet integral," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 22-25.
    • Handle: RePEc:eee:stapro:v:104:y:2015:i:c:p:22-25
    DOI: 10.1016/j.spl.2015.04.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215001340
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.04.022?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324.
    2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, 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. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    2. Gilboa, Itzhak & Samuelson, Larry & Schmeidler, David, 2013. "Dynamics of inductive inference in a unified framework," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1399-1432.
    3. Junyi Chai & Zhiquan Weng & Wenbin Liu, 2021. "Behavioral Decision Making in Normative and Descriptive Views: A Critical Review of Literature," JRFM, MDPI, vol. 14(10), pages 1-14, October.
    4. Crès, Hervé & Tvede, Mich, 2022. "Aggregation of opinions in networks of individuals and collectives," Journal of Economic Theory, Elsevier, vol. 199(C).
    5. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    6. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    7. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    8. Takao Asano & Xiaojing Cai & Ryuta Sakemoto, 2023. "Time-varying ambiguity shocks and business cycles," KIER Working Papers 1094, Kyoto University, Institute of Economic Research.
    9. Takao Asano & Hiroyuki Kojima, 2022. "Choquet Integrals and Belief Functions," KIER Working Papers 1077, Kyoto University, Institute of Economic Research.
    10. Wolitzky, Alexander, 2016. "Mechanism design with maxmin agents: theory and an application to bilateral trade," Theoretical Economics, Econometric Society, vol. 11(3), September.
    11. Xiangyu Qu, 2017. "Separate aggregation of beliefs and values under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 503-519, February.
    12. Zappia, Carlo, 2021. "Leonard Savage, The Ellsberg Paradox, And The Debate On Subjective Probabilities: Evidence From The Archives," Journal of the History of Economic Thought, Cambridge University Press, vol. 43(2), pages 169-192, June.
    13. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.
    14. Barnett, William A. & Han, Qing & Zhang, Jianbo, 2021. "Monetary services aggregation under uncertainty: A behavioral economics extension using Choquet expectation," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 437-447.
    15. Millner, Antony & Dietz, Simon & Heal, Geoffrey, 2010. "Ambiguity and climate policy," LSE Research Online Documents on Economics 37595, London School of Economics and Political Science, LSE Library.
    16. Costis Skiadas, 2013. "Smooth Ambiguity Aversion toward Small Risks and Continuous-Time Recursive Utility," Journal of Political Economy, University of Chicago Press, vol. 121(4), pages 000.
    17. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    18. Ruodu Wang & Ričardas Zitikis, 2021. "An Axiomatic Foundation for the Expected Shortfall," Management Science, INFORMS, vol. 67(3), pages 1413-1429, March.
    19. Ekaterina Svetlova & Henk van Elst, 2014. "Decision-theoretic approaches to non-knowledge in economics," Papers 1407.0787, arXiv.org.
    20. Gerasimou, Georgios, 2015. "A Characterization of Risk-Neutral and Ambiguity-Averse Behavior," MPRA Paper 68159, University Library of Munich, Germany.
    21. Ali al-Nowaihi & Sanjit Dhami & Mengxing Wei, 2018. "Quantum Decision Theory and the Ellsberg Paradox," CESifo Working Paper Series 7158, CESifo.

    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:stapro:v:104:y:2015:i:c:p:22-25. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.