Monotone Risk Aversion
21 Pages Posted: 1 Jul 2004
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Monotone Risk Aversion
Date Written: October 2003
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.
Keywords: Absolute risk aversion, relative risk aversion, decreasing risk aversion, increasing risk aversion, cumulative absolute risk aversion, cumulative relative risk aversion
JEL Classification: D81
Suggested Citation: Suggested Citation