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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.
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    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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    Cited by:

    1. Keenan, Donald C. & Snow, Arthur, 2017. "Greater parametric downside risk aversion," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 119-128.
    2. 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.
    3. 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.
    4. Jouini, Elyès & Napp, Clotilde & Nocetti, Diego, 2013. "On multivariate prudence," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1255-1267.
    5. Keenan, Donald C. & Snow, Arthur, 2024. "Full downside risk aversion," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 93-101.
    6. 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.
    7. 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.
    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. 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).
    10. 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.
    11. Jindapon, Paan, 2010. "Prudence probability premium," Economics Letters, Elsevier, vol. 109(1), pages 34-37, October.
    12. 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.
    13. 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.
    14. 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.
    15. De Donno, Marzia & Menegatti, Mario, 2024. "Preferences on discounting under time risk," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    16. 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.
    17. Keenan, Donald C. & Snow, Arthur, 2022. "Reversibly greater downside risk aversion by a prudence-based measure," Economics Letters, Elsevier, vol. 210(C).
    18. 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.
    19. 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.
    20. 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.
    21. 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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