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.
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Bibliographic InfoPaper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 03-10.
Length: 19 pages
Date of creation: Jan 2003
Date of revision:
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Other versions of this item:
- Nielsen, Lars Tyge, 1997. "Monotone Risk Aversion," CEPR Discussion Papers, C.E.P.R. Discussion Papers 1651, C.E.P.R. Discussion Papers.
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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- Minqiang Li, 2014.
"On Aumann and Serrano’s economic index of risk,"
Economic Theory, Springer,
Springer, vol. 55(2), pages 415-437, February.
- Würth, Andreas & Schumacher, J.M., 2011.
"Risk aversion for nonsmooth utility functions,"
Journal of Mathematical Economics,
Elsevier, vol. 47(2), pages 109-128, March.
- Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics.
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