IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v60y2015icp74-80.html
   My bibliography  Save this article

Differentiability of von Neumann–Morgenstern utility functions

Author

Listed:
  • Nakamura, Yutaka

Abstract

This paper studies necessary and sufficient preference-based conditions for differentiability of risk averse (prudent, or temperate) von Neumann–Morgenstern utility functions. The very idea to devise those conditions is based on the reverse claim of an old observation by Arrow that a risk-averse expected-utility maximizer will always accept a sufficiently small stake in any positive expected-value bet if her von Neumann–Morgenstern utility function is differentiable.

Suggested Citation

  • Nakamura, Yutaka, 2015. "Differentiability of von Neumann–Morgenstern utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 74-80.
    • Handle: RePEc:eee:mateco:v:60:y:2015:i:c:p:74-80
    DOI: 10.1016/j.jmateco.2015.06.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406815000634
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2015.06.008?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. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    2. Lars Tyge Nielsen, 1999. "Differentiable von Neumann-Morgenstern utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 285-296.
    3. Eeckhoudt, Louis & Gollier, Christian & Schneider, Thierry, 1995. "Risk-aversion, prudence and temperance: A unified approach," Economics Letters, Elsevier, vol. 48(3-4), pages 331-336, June.
    4. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wei Ma, 2018. "Random Expected Utility Theory with a Continuum of Prizes," Working Papers 201854, University of Pretoria, Department of Economics.
    2. Wei Ma, 2018. "Random expected utility theory with a continuum of prizes," Annals of Operations Research, Springer, vol. 271(2), pages 787-809, December.
    3. Wei Ma, 2018. "Random Expected Utility Theory with a Continuum of Prizes," Working Papers 760, Economic Research Southern Africa.

    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. Bonilla, Claudio A. & Vergara, Marcos, 2013. "Credit rationing or entrepreneurial risk aversion? A comment," Economics Letters, Elsevier, vol. 120(2), pages 329-331.
    2. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    3. Loubergé, Henri & Malevergne, Yannick & Rey, Béatrice, 2020. "New Results for additive and multiplicative risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 140-151.
    4. Danau, Daniel, 2020. "Prudence and preference for flexibility gain," European Journal of Operational Research, Elsevier, vol. 287(2), pages 776-785.
    5. Louis R. Eeckhoudt & Roger J. A. Laeven, 2021. "Probability Premium and Attitude Towards Probability," Papers 2105.00054, arXiv.org.
    6. Patricia Apps & Yuri Andrienko & Ray Rees, 2014. "Risk and Precautionary Saving in Two-Person Households," American Economic Review, American Economic Association, vol. 104(3), pages 1040-1046, March.
    7. Thomas Mayrhofer & Hendrik Schmitz, 2020. "Prudence and prevention - Empirical evidence," Working Papers CIE 134, Paderborn University, CIE Center for International Economics.
    8. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    9. Li, Jingyuan, 2011. "The demand for a risky asset in the presence of a background risk," Journal of Economic Theory, Elsevier, vol. 146(1), pages 372-391, January.
    10. Patrick Roger, 2011. "Mixed risk aversion and preference for risk disaggregation: a story of moments," Theory and Decision, Springer, vol. 70(1), pages 27-44, January.
    11. Christophe Courbage & Béatrice Rey, 2010. "On Non‐Monetary Measures In The Face Of Risks And The Signs Of The Derivatives," Bulletin of Economic Research, Wiley Blackwell, vol. 62(3), pages 295-304, July.
    12. Malevergne, Y. & Rey, B., 2009. "On cross-risk vulnerability," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 224-229, October.
    13. Baiardi, Donatella & De Donno, Marzia & Magnani, Marco & Menegatti, Mario, 2015. "New results on precautionary saving under two risks," Economics Letters, Elsevier, vol. 130(C), pages 17-20.
    14. Bottasso, Anna & Duchêne, Sébastien & Guerci, Eric & Hanaki, Nobuyuki & Noussair, Charles N., 2022. "Higher order risk attitudes of financial experts," Journal of Behavioral and Experimental Finance, Elsevier, vol. 34(C).
    15. Christian Gollier & Miles S. Kimball, 2018. "Toward a Systematic Approach to the Economic Effects of Risk: Characterizing Utility Functions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(2), pages 397-430, June.
    16. 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.
    17. Irina Georgescu, 2018. "The Effect of Prudence on the Optimal Allocation in Possibilistic and Mixed Models," Mathematics, MDPI, vol. 6(8), pages 1-19, August.
    18. Monica Billio & Bertrand Maillet & Loriana Pelizzon, 2022. "A meta-measure of performance related to both investors and investments characteristics," Annals of Operations Research, Springer, vol. 313(2), pages 1405-1447, June.
    19. Mario Menegatti & Richard Peter, 2022. "Changes in Risky Benefits and in Risky Costs: A Question of the Right Order," Management Science, INFORMS, vol. 68(5), pages 3625-3634, May.
    20. Eeckhoudt, Louis R. & Laeven, Roger J.A. & Schlesinger, Harris, 2020. "Risk apportionment: The dual story," Journal of Economic Theory, Elsevier, vol. 185(C).

    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:60:y:2015:i:c:p:74-80. 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.