IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v102y2022ics0304406822000854.html
   My bibliography  Save this article

On the relationship between comparisons of risk aversion of different orders

Author

Listed:
  • De Donno, Marzia
  • Menegatti, Mario

Abstract

We show conditions which ensure that the comparisons between risk aversion of different orders of two decision makers are related. In particular, we derive a condition ensuring that greater downside risk aversion implies greater risk aversion and a different condition ensuring that the opposite implication holds. We then generalize these results to higher order greater risk aversion, obtaining conditions which make it possible to infer the direction of the comparison for risk aversion of a given order from the knowledge of the direction for a different order.

Suggested Citation

  • De Donno, Marzia & Menegatti, Mario, 2022. "On the relationship between comparisons of risk aversion of different orders," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    • Handle: RePEc:eee:mateco:v:102:y:2022:i:c:s0304406822000854
    DOI: 10.1016/j.jmateco.2022.102757
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406822000854
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2022.102757?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. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    2. Peter C. Fishburn, 1976. "Unbounded Utility Functions in Expected Utility Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 163-168.
    3. Keenan, Donald C. & Snow, Arthur, 2022. "Reversibly greater downside risk aversion by a prudence-based measure," Economics Letters, Elsevier, vol. 210(C).
    4. Keenan, Donald C & Snow, Arthur, 2002. "Greater Downside Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 267-277, May.
    5. Liqun Liu & Jack Meyer, 2012. "Decreasing absolute risk aversion, prudence and increased downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 44(3), pages 243-260, June.
    6. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    7. Menegatti, Mario, 2015. "New results on high-order risk changes," European Journal of Operational Research, Elsevier, vol. 243(2), pages 678-681.
    8. Keenan, Donald C. & Snow, Arthur, 2009. "Greater downside risk aversion in the large," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1092-1101, May.
    9. Kenneth J. Arrow, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 136-138.
    10. Donald C. Keenan & Arthur Snow, 2022. "Reversibly greater downside risk aversion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 47(2), pages 327-338, September.
    11. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    12. Donald C. Keenan & Arthur Snow, 2016. "Strong Increases in Downside Risk Aversion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 41(2), pages 149-161, September.
    13. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    14. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    15. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    16. Keenan, Donald C. & Snow, Arthur, 2018. "Bringing order to rankings of utility functions by strong increases in nth order aversion to risk," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 35-44.
    17. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
    18. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    19. Peter Wakker, 1993. "Unbounded Utility for Savage's “Foundations of Statistics,” and Other Models," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 446-485, May.
    20. Terence M. Ryan, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 133-135.
    21. Marzia Donno & Marco Magnani & Mario Menegatti, 2020. "Changes in multiplicative risks and optimal portfolio choice: new interpretations and results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 251-267, June.
    22. Leigh Tesfatsion, 1976. "Stochastic Dominance and the Maximization of Expected Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(2), pages 301-315.
    23. Marzia De Donno & Mario Menegatti, 2020. "Some conditions for the equivalence between risk aversion, prudence and temperance," Theory and Decision, Springer, vol. 89(1), pages 39-60, July.
    24. Claude Toulet, 1986. "An Axiomatic Model of Unbounded Utility Functions," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 81-94, February.
    25. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    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. De Donno, Marzia & Menegatti, Mario, 2024. "Preferences on discounting under time risk," Journal of Mathematical Economics, Elsevier, vol. 113(C).

    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. De Donno, Marzia & Menegatti, Mario, 2024. "Preferences on discounting under time risk," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    2. Keenan, Donald C. & Snow, Arthur, 2024. "Full downside risk aversion," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 93-101.
    3. Liqun Liu & William S. Neilson, 2019. "Alternative Approaches to Comparative n th-Degree Risk Aversion," Management Science, INFORMS, vol. 65(8), pages 3824-3834, August.
    4. Keenan, Donald C. & Snow, Arthur, 2022. "Reversibly greater downside risk aversion by a prudence-based measure," Economics Letters, Elsevier, vol. 210(C).
    5. Donald C. Keenan & Arthur Snow, 2016. "Strong Increases in Downside Risk Aversion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 41(2), pages 149-161, September.
    6. Marzia De Donno & Mario Menegatti, 2020. "Some conditions for the equivalence between risk aversion, prudence and temperance," Theory and Decision, Springer, vol. 89(1), pages 39-60, July.
    7. 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.
    8. Liu, Liqun & Meyer, Jack, 2013. "Substituting one risk increase for another: A method for measuring risk aversion," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2706-2718.
    9. Richard Peter, 2021. "Who should exert more effort? Risk aversion, downside risk aversion and optimal prevention," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1259-1281, June.
    10. 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.
    11. Peter, Richard & Hofmann, Annette, 2024. "Precautionary risk-reduction and saving decisions: Two sides of the same coin?," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 175-194.
    12. James Huang & Richard Stapleton, 2017. "Higher-order risk vulnerability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 387-406, February.
    13. Keenan, Donald C. & Snow, Arthur, 2018. "Bringing order to rankings of utility functions by strong increases in nth order aversion to risk," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 35-44.
    14. Marzia Donno & Marco Magnani & Mario Menegatti, 2020. "Changes in multiplicative risks and optimal portfolio choice: new interpretations and results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 251-267, June.
    15. 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.
    16. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    17. Donald C. Keenan & Arthur Snow, 2022. "Reversibly greater downside risk aversion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 47(2), pages 327-338, September.
    18. Keenan, Donald C. & Snow, Arthur, 2017. "Greater parametric downside risk aversion," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 119-128.
    19. Menegatti, Mario, 2023. "Variability in punishment, risk preferences and crime deterrence," International Review of Law and Economics, Elsevier, vol. 75(C).
    20. Michel Denuit & Liqun Liu, 2014. "Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance," Theory and Decision, Springer, vol. 76(2), pages 287-295, February.

    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:102:y:2022:i:c:s0304406822000854. 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.