Monotone risk aversion

Summary. 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.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.