Monotone risk aversion
AbstractThis 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
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Bibliographic InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 25 (2005)
Issue (Month): 1 (01)
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- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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- Li, Minqiang, 2013. "On Aumann and Serrano's Economic Index of Risk," MPRA Paper 47466, University Library of Munich, Germany.
- Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics.
- Würth, Andreas & Schumacher, J.M., 2011.
"Risk aversion for nonsmooth utility functions,"
Journal of Mathematical Economics,
Elsevier, vol. 47(2), pages 109-128, March.
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