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Monotone Risk Aversion

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  • Lars Tyge Nielsen

Abstract

This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 03-10.

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Length: 19 pages
Date of creation: Jan 2003
Date of revision:
Handle: RePEc:kud:kuiedp:0310

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Cited by:
  1. Minqiang Li, 2014. "On Aumann and Serrano’s economic index of risk," Economic Theory, Springer, Springer, vol. 55(2), pages 415-437, February.
  2. Würth, Andreas & Schumacher, J.M., 2011. "Risk aversion for nonsmooth utility functions," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 109-128, March.
  3. Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics.

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