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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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 3 (May)
Pages: 1092-1101

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:3:p:1092-1101

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Downside risk Risk aversion Arrow-Pratt Diamond-Stiglitz;

References

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  1. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
  2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  3. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-32, December.
  4. 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.
  5. Keenan, Donald C & Snow, Arthur, 2002. " Greater Downside Risk Aversion," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 267-77, May.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  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 621-38, May.
  8. Modica, Salvatore & Scarsini, Marco, 2005. "A note on comparative downside risk aversion," Journal of Economic Theory, Elsevier, vol. 122(2), pages 267-271, June.
  9. 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.
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Citations

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Cited by:
  1. Elyès Jouini & Clotilde Napp & Diego Nocetti, 2011. "On Multivariate Prudence," Working Papers halshs-00635558, HAL.
  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. Jindapon, Paan, 2010. "Prudence probability premium," Economics Letters, Elsevier, vol. 109(1), pages 34-37, October.
  5. 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.
  6. 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.

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