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Broadly Decreasing Risk Aversion

Author

Listed:
  • Gregory M. Gelles

    (Department of Economics, 101 Harris Hall, University of Missouri-Rolla, Rolla, Missouri 65409-1250)

  • Douglas W. Mitchell

    (Department of Economics, West Virginia University, Morgantown, West Virginia 26506-6025)

Abstract

This paper considers decision-making in the presence of two additive risk sources, with no restrictions on the relation between the two risks. A utility function is said to exhibit broad DARA if and only if a rise in wealth always decreases the magnitude of the risk premium for one of the risks vis-a-vis the other. A condition on utility functions giving this property is derived: utility must be of the linear plus exponential form. It is shown that certain problems involving portfolios and risk-averse firms give unambiguous comparative statics if and only if utility exhibits broad DARA.

Suggested Citation

  • Gregory M. Gelles & Douglas W. Mitchell, 1999. "Broadly Decreasing Risk Aversion," Management Science, INFORMS, vol. 45(10), pages 1432-1439, October.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:10:p:1432-1439
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    File URL: http://dx.doi.org/10.1287/mnsc.45.10.1432
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    References listed on IDEAS

    as
    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. Sandmo, Agnar, 1971. "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review, American Economic Association, vol. 61(1), pages 65-73, March.
    3. 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.
    4. David E. Bell, 1988. "One-Switch Utility Functions and a Measure of Risk," Management Science, INFORMS, vol. 34(12), pages 1416-1424, December.
    5. David E. Bell, 1995. "A Contextual Uncertainty Condition for Behavior Under Risk," Management Science, INFORMS, vol. 41(7), pages 1145-1150, July.
    6. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    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. Kihlstrom, Richard E & Romer, David & Williams, Steve, 1981. "Risk Aversion with Random Initial Wealth," Econometrica, Econometric Society, vol. 49(4), pages 911-920, June.
    10. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. David E. Bell & Peter C. Fishburn, 2001. "Strong One-Switch Utility," Management Science, INFORMS, vol. 47(4), pages 601-604, April.
    2. Martin Bohner & Gregory Gelles, 2012. "Risk aversion and risk vulnerability in the continuous and discrete case," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(1), pages 1-28, May.
    3. Conniffe, Denis, 2008. "Generalised Means of Simple Utility Functions with Risk Aversion," The Economic and Social Review, Economic and Social Studies, vol. 39(1), pages 1-12.
    4. Gelles, Gregory M. & Mitchell, Douglas W., 2002. "Increasingly mean-seeking utility functions and n-asset portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 42(5), pages 911-919.
    5. Keenan, Donald C. & Snow, Arthur, 2012. "Ross risk vulnerability for introductions and changes in background risk," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 197-206.

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