Monotone Risk Aversion

Lars Nielsen

No 1651, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: This paper shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with a positive and absolutely continuous derivative. The cumulative absolute risk aversion function, which is defined as the negative of the logarithm of the marginal utility, will also be absolutely continuous. Its density, called the absolute risk aversion density, is a generalization of the coefficient of absolute risk aversion, and it is well defined almost everywhere. A strictly increasing and 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 convenient characterization of all such utility functions. Analogues of all the results also hold for increasing absolute risk aversion, as well as for increasing and decreasing relative risk aversion.

Keywords: Decreasing Absolute Risk Aversion; Risk Aversion (search for similar items in EconPapers)
JEL-codes: D81 (search for similar items in EconPapers)
Date: 1997-05
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Related works:
Chapter: Monotone Risk Aversion (2006)
Journal Article: Monotone risk aversion (2005)
Working Paper: Monotone Risk Aversion (2003)
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