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Greater downside risk aversion in the large

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  • Keenan, Donald C.
  • Snow, Arthur

Abstract

In this paper, we advance a definition of greater downside risk aversion that applies to both large and small changes in risk preference, and thereby complements the results for small changes reported previously. We show that a downside risk-averse transformation of a utility function results in a function that is more downside risk averse in the same manner that a risk-averse transformation increases risk aversion. Our demonstration is conducted first by using the compensated approach introduced by Diamond and Stiglitz [P. Diamond, J. Stiglitz, Increases in risk and in risk aversion, J. Econ. Theory 8 (1974) 337-360] and then by using an adaptation of the risk premium approach taken by Pratt [J. Pratt, Risk aversion in the small and in the large, Econometrica 32 (1964) 122-136].

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  • 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.
    • Handle: RePEc:eee:jetheo:v:144:y:2009:i:3:p:1092-1101
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    References listed on IDEAS

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    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. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
    3. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    4. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 82(3), pages 465-473.
    5. Keenan, Donald C & Snow, Arthur, 2002. "Greater Downside Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 267-277, May.
    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. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    8. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    9. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-932, December.
    10. Jindapon, Paan & Neilson, William S., 2007. "Higher-order generalizations of Arrow-Pratt and Ross risk aversion: A comparative statics approach," Journal of Economic Theory, Elsevier, vol. 136(1), pages 719-728, September.
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    Citations

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    Cited by:

    1. Donald Keenan & Arthur Snow, 2012. "The Schwarzian derivative as a ranking of downside risk aversion," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 149-160, April.
    2. Keenan, Donald C. & Snow, Arthur, 2010. "Greater prudence and greater downside risk aversion," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2018-2026, September.
    3. Jouini, Elyès & Napp, Clotilde & Nocetti, Diego, 2013. "On multivariate prudence," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1255-1267.
    4. 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.
    5. 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).
    6. 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.
    7. Keenan, Donald C. & Snow, Arthur, 2022. "Reversibly greater downside risk aversion by a prudence-based measure," Economics Letters, Elsevier, vol. 210(C).
    8. 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.
    9. 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.
    10. Keenan, Donald C. & Snow, Arthur, 2017. "Greater parametric downside risk aversion," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 119-128.
    11. Emmanuelle Augeraud‐Véron & Marc Leandri, 2024. "Optimal self‐protection and health risk perceptions: Exploring connections between risk theory and the Health Belief Model," Health Economics, John Wiley & Sons, Ltd., vol. 33(7), pages 1565-1583, July.
    12. 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.
    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. Jindapon, Paan, 2010. "Prudence probability premium," Economics Letters, Elsevier, vol. 109(1), pages 34-37, October.
    15. 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.
    16. Richard Peter, 2024. "The economics of self-protection," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 49(1), pages 6-35, March.
    17. 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.
    18. Richard Peter, 2021. "A fresh look at primary prevention for health risks," Health Economics, John Wiley & Sons, Ltd., vol. 30(5), pages 1247-1254, May.
    19. Richard Watt & Francisco J. Vazquez, 2013. "Allocative downside risk aversion," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(4), pages 267-277, December.

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