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Greater prudence and greater downside risk aversion

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  • Keenan, Donald C.
  • Snow, Arthur

Abstract

Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=-u'''/u'', is related to downside risk aversion, which is indicated by a positive value for u'''. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:5:p:2018-2026
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    References listed on IDEAS

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    Cited by:

    1. repec:eee:ecolet:v:157:y:2017:i:c:p:14-16 is not listed on IDEAS
    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. Gollier, Christian & Kimball, Miles S., 2018. "Toward a Systematic Approach to the Economic Effects of Risk: Characterizing Utility Functions"," TSE Working Papers 18-909, Toulouse School of Economics (TSE).
    4. 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.
    5. Pierre Chaigneau, 2012. "The Effect of Risk Preferences on the Valuation and Incentives of Compensation Contracts," Cahiers de recherche 1209, CIRPEE.
    6. Jindapon, Paan, 2010. "Prudence probability premium," Economics Letters, Elsevier, vol. 109(1), pages 34-37, October.
    7. 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.
    8. Pierre Chaigneau, 2012. "The effect of risk preferences on the valuation and incentives of compensation contracts," FMG Discussion Papers dp697, Financial Markets Group.
    9. Pierre Chaigneau & Louis Eeckhoudt, 2015. "Downside Risk Neutral Probabilities," Cahiers de recherche 1521, CIRPEE.
    10. 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.
    11. 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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    Keywords

    Downside risk aversion Prudence;

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