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Preferences and Increased Risk Aversion under a General Framework of Stochastic Dominance

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  • Donald C., Rudow

Abstract

This paper analyzes increased risk aversion in the presence of two risks. Necessary and sufficient conditions for increased risk aversion across the domain of the foreground risk are found for changes in both the foreground and background risks. Preferences that satisfy the necessary and sufficient conditions are determined through a lower bound on their measure of prudence. These bounds are found through second-degree spreads of a transformation of the background risk. The necessary and sufficient conditions demonstrate that for all second degree spreads of this nature, absolute temperance plays a central role in the necessary and sufficient conditions for increased risk aversion. The approach also demonstrates that changes in risk aversion under the general framework of stochastic dominating spreads can be explained by a weighted average of terms involving absolute prudence and absolute temperance. Once a general set of necessary and sufficient conditions have been found it is shown that for preferences that are decreasing absolute risk averse in the sense of Ross, increased risk aversion due to changes in the background risk within this framework is equivalent to Ross risk vulnerability. The general conditions also find necessary and sufficient conditions for preferences to be properly risk averse toward patent increases in risk.

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File URL: http://mpra.ub.uni-muenchen.de/41191/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41191.

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Date of creation: 07 Jun 2005
Date of revision: 07 Jun 2005
Handle: RePEc:pra:mprapa:41191

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Related research

Keywords: Stochastic dominance; increased risk aversion; background risk; transformations; patent increase in risk; prudence; proper risk aversion; risk vulnerability;

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  1. 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.
  2. Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-27, March.
  3. Donald C. Keenan & Arthur Snow, 2003. "Locally Greater Vulnerability to Background Risk," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 28(2), pages 161-172, December.
  4. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-23, September.
  5. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
  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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