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Weak Proper Risk Aversion And The Tempering Effect of Background Risk

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Listed:
  • Gollier, Christian
  • John W. PRATT

Abstract

We examine in this paper a new natural restriction on utility functions, namely that an undesirable risk can never be made desirable by the presence of an independent, unfair risk. This concept is called weak properness. It generalizes the concept of properness (individually undesirable, independent risks are always jointly undesirable) introduced by Pratt and Zeckhauser [1987]. An important property of weak properness and properness is that adding an unfair risk to wealth makes risk-averse people more risk averse, therefore increasing the equilibrium price of risk in exchange economies a la Lucas [1978]. Weak properness implies that the two first derivatives of the utility function are concave transformations of the original utility function. A sufficient condition for weak-properness is that absolute risk aversion be decreasing and convex.

Suggested Citation

  • Gollier, Christian & John W. PRATT, 1993. "Weak Proper Risk Aversion And The Tempering Effect of Background Risk," Working Papers 018, Risk and Insurance Archive.
  • Handle: RePEc:wop:riskar:018
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    References listed on IDEAS

    as
    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    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. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    4. 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.
    5. 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.
    6. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
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    Cited by:

    1. Gollier, Christian, 1994. "Dynamic Risk Taking With Indivisible Risks," Working Papers 013, Risk and Insurance Archive.
    2. Luigi Guiso & Tullio Jappelli, 2000. "Household Portfolios in Italy," CSEF Working Papers 43, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    3. Eeckhoudt, Louis & Gollier, Christian & Schneider, Thierry, 1995. "Risk-aversion, prudence and temperance: A unified approach," Economics Letters, Elsevier, vol. 48(3-4), pages 331-336, June.
    4. 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.

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