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Weak Proper Risk Aversion And The Tempering Effect of Background Risk

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Author Info
Gollier, Christian
John W. PRATT

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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.

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Paper provided by Risk and Insurance Archive in its series Working Papers with number 018.

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Date of creation: Oct 1993
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Handle: RePEc:wop:riskar:018

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Keywords: background risk proper risk aversion standard risk aversion.

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March. [Downloadable!] (restricted)
  2. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January. [Downloadable!] (restricted)
  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. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January. [Downloadable!] (restricted)
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  5. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December. [Downloadable!] (restricted)
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  1. Gollier, Christian, 1994. "Dynamic Risk Taking With Indivisible Risks," Working Papers 013, Risk and Insurance Archive. [Downloadable!]
  2. Luigi Guiso & Tullio Jappelli, 2000. "Household Portfolios in Italy," CSEF Working Papers 43, Centre for Studies in Economics and Finance (CSEF), University of Salerno, Italy. [Downloadable!]
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  3. EECKHOUDT, Louis & Christian GOLLIER & Harris SCHLESINGER, 1994. "Changes in Background Risk and Risk Taking Behavior," Working Papers 005, Risk and Insurance Archive. [Downloadable!]
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  4. Luc Arrondel & Stefan Lollivier, 2004. "Transaction costs, Income Risk and Household Portfolio Allocation: Evidence from French Panel Data," DELTA Working Papers 2004-19, DELTA (Ecole normale supérieure). [Downloadable!]
  5. Luc Arrondel & Hector Calvo-Pardo, 2002. "Portfolio Choice with a Correlated Background Risk : Theory and Evidence," DELTA Working Papers 2002-16, DELTA (Ecole normale supérieure). [Downloadable!]
  6. EECKHOUDT, Louis & Christian GOLLIER & Thierry SCHNEIDER, 1994. "Risk Aversion, Prudence and Temperance : A Unified Approach," Working Papers 006, Risk and Insurance Archive. [Downloadable!]
    Other versions:
  7. Günter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 2005. "Incremental Risk Vulnerability," CoFE Discussion Paper 05-08, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
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