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Standard Risk Aversion

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  • Kimball, Miles S

Abstract

This paper introduces the concept of standard risk aversion. A von Neumann-Morgenstern utility function has standard risk aversion if every risk that has a negative interaction with a small reduction in wealth also has a negative interaction with any undesirable, independent risk. 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' (an undesirable risk always remaining undesirable in the presence of an independent undesirable risk), but also that being forced to face an undesirable risk reduces the optimal investment in a risky security with an independent return. Copyright 1993 by The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 61 (1993)
Issue (Month): 3 (May)
Pages: 589-611

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Handle: RePEc:ecm:emetrp:v:61:y:1993:i:3:p:589-611

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  1. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  2. 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.
  3. Bagnoli, M. & Bergstrom, T., 1989. "Log-Concave Probability And Its Applications," Papers 89-23, Michigan - Center for Research on Economic & Social Theory.
  4. Pratt, John W, 1990. " The Logic of Partial-Risk Aversion: Paradox Lost," Journal of Risk and Uncertainty, Springer, vol. 3(2), pages 105-13, June.
  5. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
  6. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
  7. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-20, June.
  8. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January.
  9. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
  10. 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.
  11. Sandmo, Agnar, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Wiley Blackwell, vol. 37(3), pages 353-60, July.
  12. 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.
  13. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
  14. Nachman, David C., 1982. "Preservation of "more risk averse" under expectations," Journal of Economic Theory, Elsevier, vol. 28(2), pages 361-368, December.
  15. 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.
  16. Miles S. Kimball, 1991. "Precautionary Motives for Holding Assets," NBER Working Papers 3586, National Bureau of Economic Research, Inc.
  17. Miles S. Kimball, 1990. "Precautionary Saving and the Marginal Propensity to Consume," NBER Working Papers 3403, National Bureau of Economic Research, Inc.
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