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Weak Proper Risk Aversion And The Tempering Effect of Background Risk

  • Gollier, Christian
  • John W. PRATT

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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  1. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  2. DREZE, Jacques H. & MODIGLIANI, Franco, . "Cosumption decisions under uncertainty," CORE Discussion Papers RP -119, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
  4. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-54, January.
  5. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-89, May.
  6. 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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