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Monotone Risk Aversion


  • Nielsen, Lars Tyge


This paper shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with a positive and absolutely continuous derivative. The cumulative absolute risk aversion function, which is defined as the negative of the logarithm of the marginal utility, will also be absolutely continuous. Its density, called the absolute risk aversion density, is a generalization of the coefficient of absolute risk aversion, and it is well defined almost everywhere. A strictly increasing and 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 convenient characterization of all such utility functions. Analogues of all the results also hold for increasing absolute risk aversion, as well as for increasing and decreasing relative risk aversion.

Suggested Citation

  • Nielsen, Lars Tyge, 1997. "Monotone Risk Aversion," CEPR Discussion Papers 1651, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:1651

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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


    Decreasing Absolute Risk Aversion; Risk Aversion;

    JEL classification:

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


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