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Monotone risk aversion

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  • Lars Nielsen

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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. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(1), pages 203-215, January.
  • Handle: RePEc:spr:joecth:v:25:y:2005:i:1:p:203-215
    DOI: 10.1007/s00199-004-0471-y
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    File URL: http://hdl.handle.net/10.1007/s00199-004-0471-y
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    Cited by:

    1. Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics.
    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. Minqiang Li, 2014. "On Aumann and Serrano’s economic index of risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 415-437, February.

    More about this item

    Keywords

    Absolute risk aversion; Relative risk aversion; Decreasing risk aversion; Increasing risk aversion; Cumulative absolute risk aversion; Cumulative relative risk aversion.;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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