Monotone Risk Aversion

21 Pages Posted: 1 Jul 2004

Multiple version iconThere are 2 versions of this paper

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

Nielsen, Lars Tyge, Monotone Risk Aversion (October 2003). Available at SSRN: https://ssrn.com/abstract=491702 or http://dx.doi.org/10.2139/ssrn.491702

Lars Tyge Nielsen (Contact Author)

Columbia University

3022 Broadway
New York, NY 10027
United States

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