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.
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Paper 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: Handle: RePEc:kud:kuiedp:0310
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