IDEAS home Printed from https://ideas.repec.org/a/aag/wpaper/v24y2020i3p142-217.html
   My bibliography  Save this article

Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions

Author

Listed:
  • Fausto Corradin

    (GRETA Associates, University Ca’ Foscari of Venice)

  • Domenico Sartore

    (University Ca’ Foscari of Venice)

Abstract

The condition of Risk Aversion implies that the Utility Function must be concave. We take into account the dependence of the Utility Function on the return that has any type of two-parameter distribution; it is possible to define Risk and Target, the first one may be the Standard Deviation of the return and the last one usually is the Expected value of the return, as a generic function of these two parameters. Considering the 3D space of Risk, Target and Expected Utility, this paper determines the Differential Conditions for these three functions so that the Expected Utility Function depends decreasingly on Risk and increasingly on Target, that means the iso-utility curves have positive slope in the plane of Risk and Target. As a particular case, we discuss these conditions in the case of the CRRA Utility Function and the Truncated Normal distribution. Furthermore, different measures of Risk are chosen, as Value at Risk (VaR) and Expected Shortfall (ES), to verify if these measures maintain a positive slope of the Iso-utility curves in the Risk-Target plane.

Suggested Citation

  • Fausto Corradin & Domenico Sartore, 2020. "Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(3), pages 142-217, September.
    • Handle: RePEc:aag:wpaper:v:24:y:2020:i:3:p:142-217
    as

    Download full text from publisher

    File URL: https://iads.site/Risk-Aversion-Differential-Conditions-for-the-Iso-Utility-Curves-with-Positive-Slope-in-Transformed-Two-Parameter-Distributions
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Lars Tyge Nielsen & Fatma Lajeri, 2000. "Parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 469-476.
    3. LiCalzi, Marco & Sorato, Annamaria, 2006. "The Pearson system of utility functions," European Journal of Operational Research, Elsevier, vol. 172(2), pages 560-573, July.
    4. Fausto Corradin & Domenico Sartore, 2014. "Fund Ratings: The method reconsidered," Working Papers 2014:17, Department of Economics, University of Venice "Ca' Foscari".
    5. Montesano, Aldo, 1991. "Measures of Risk Aversion with Expected and Nonexpected Utility," Journal of Risk and Uncertainty, Springer, vol. 4(3), pages 271-283, July.
    6. Fausto Corradin & Domenico Sartore, 2016. "Weak Dependence of CRRA on Standard Deviation in the Case of Truncated Normal Distribution of Returns," Working Papers 2016:18, Department of Economics, University of Venice "Ca' Foscari".
    7. Thomas Eichner & Andreas Wagener, 2003. "More on parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 895-900, June.
    8. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    9. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    10. Fausto Corradin & Domenico Sartore, 2016. "Non Central Moments of the Truncated Normal Variable," Working Papers 2016:17, Department of Economics, University of Venice "Ca' Foscari".
    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. Fausto Corradin & Domenico Sartore, 2020. "Risk Aversion: Differential Conditions for the Iso-Utility Curves with Positive Slope in Transformed Two-Parameter Distributions," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(3), pages 142-217, September.
    2. Vergara, Marcos & Bonilla, Claudio A., 2021. "Precautionary saving in mean-variance models and different sources of risk," Economic Modelling, Elsevier, vol. 98(C), pages 280-289.
    3. Alain Chateauneuf & Ghizlane Lakhnati & Eric Langlais, 2016. "On the precautionary motive for savings and prudence in the rank-dependent utility framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 169-182, January.
    4. Bonilla, Claudio A. & Ruiz, Jose L., 2014. "Insurance demand and first order risk increases under (μ,σ)-preferences," Finance Research Letters, Elsevier, vol. 11(3), pages 219-223.
    5. Wagener, Andreas, 2003. "Comparative statics under uncertainty: The case of mean-variance preferences," European Journal of Operational Research, Elsevier, vol. 151(1), pages 224-232, November.
    6. Wing-Keung Wong & Chenghu Ma, 2008. "Preferences over location-scale family," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 119-146, October.
    7. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    8. 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.
    9. Peter, Richard, 2017. "Optimal self-protection in two periods: On the role of endogenous saving," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 19-36.
    10. Kubitza, Christian & Hofmann, Annette & Steinorth, Petra, 2019. "Financial literacy and precautionary insurance," ICIR Working Paper Series 34/19, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    11. Jean-Daniel Guigou & Bruno Lovat & Nicolas Treich, 2017. "Risky rents," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 151-164, October.
    12. Wong, Kit Pong, 2017. "Production and hedging under state-dependent preferences and background risk," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 527-534.
    13. Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
    14. Christian Gollier, 2007. "Whom should we believe? Aggregation of heterogeneous beliefs," Journal of Risk and Uncertainty, Springer, vol. 35(2), pages 107-127, October.
    15. Claudio Bonilla & Marcos Vergara, 2022. "New results on precautionary saving and nonlinear risks," Journal of Economics, Springer, vol. 136(2), pages 177-189, July.
    16. Caballe, Jordi & Pomansky, Alexey, 1996. "Mixed Risk Aversion," Journal of Economic Theory, Elsevier, vol. 71(2), pages 485-513, November.
    17. Mark Huggett, 2004. "Precautionary Wealth Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 769-781.
    18. Christian Gollier & Alexander Muermann, 2010. "Optimal Choice and Beliefs with Ex Ante Savoring and Ex Post Disappointment," Management Science, INFORMS, vol. 56(8), pages 1272-1284, August.
    19. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    20. Anderberg, Dan & Andersson, Fredrik, 2003. "Investments in human capital, wage uncertainty, and public policy," Journal of Public Economics, Elsevier, vol. 87(7-8), pages 1521-1537, August.

    More about this item

    Keywords

    Concavity; Differential Conditions; Expected Shortfall; Risk Aversion; Standard Deviation; Value at Risk;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

    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:aag:wpaper:v:24:y:2020:i:3:p:142-217. 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: Vincent Pan (email available below). General contact details of provider: https://edirc.repec.org/data/dfasitw.html .

    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.