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Standard Risk Aversion

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  • Miles S. Kimball

Abstract

This paper introduces the concept of standard risk aversion. A von Neumann-Morgenstern utility function has standard risk aversion if any risk makes a small reduction in wealth more painful (in the sense of an increased reduction in expected utility) also makes any undesirable, independent risk more painful. It is shown that, given monotonicity and concavity, the combination of decreasing absolute risk aversion and decreasing absolute prudence is necessary and sufficient for standard risk aversion. Standard risk aversion is shown to imply not only Pratt and Zeckhauser's 'proper risk aversion" (individually undesirable, independent risks always being jointly undesirable) , but also that being forced to face an undesirable risk reduces the optimal investment in a risky security with and independent return. Similar results are established for the effect of broad class of increases in one risk on the desirability of (or optimal investment in) a second, independent risk.

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  • Miles S. Kimball, 1991. "Standard Risk Aversion," NBER Technical Working Papers 0099, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0099
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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. Mark Bagnoli & Ted Bergstrom, 2005. "Log-concave probability and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 445-469, August.
    3. 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.
    4. Miles S. Kimball, 1991. "Precautionary Motives for Holding Assets," NBER Working Papers 3586, National Bureau of Economic Research, Inc.
    5. Mankiw, N. Gregory, 1986. "The equity premium and the concentration of aggregate shocks," Journal of Financial Economics, Elsevier, vol. 17(1), pages 211-219, September.
    6. Pratt, John W, 1990. "The Logic of Partial-Risk Aversion: Paradox Lost," Journal of Risk and Uncertainty, Springer, vol. 3(2), pages 105-113, June.
    7. Nachman, David C., 1982. "Preservation of "more risk averse" under expectations," Journal of Economic Theory, Elsevier, vol. 28(2), pages 361-368, December.
    8. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    9. Pratt, John W, 1988. "Aversion to One Risk in the Presence of Others," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 395-413, December.
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    11. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
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    13. 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.
    14. Miles S. Kimball, 1990. "Precautionary Saving and the Marginal Propensity to Consume," NBER Working Papers 3403, National Bureau of Economic Research, Inc.
    15. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    16. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-920, June.
    17. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
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