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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.

Suggested Citation

  • Lars Tyge Nielsen, 2003. "Monotone Risk Aversion," Discussion Papers 03-10, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0310
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2003/0310.pdf/
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    References listed on IDEAS

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    1. Nicolas Gravel, 2001. "On the difficulty of combining actual and potential criteria for an increase in social welfare," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 163-180.
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    9. Geanakoplos, J. & Magill, M. & Quinzii, M. & Dreze, J., 1990. "Generic inefficiency of stock market equilibrium when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 113-151.
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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

    JEL classification:

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

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