Monotone Risk Aversion

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Monotone Risk Aversion

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Lars Tyge Nielsen

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Lars Tyge Nielsen

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.

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Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 03-10.

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Length: 19 pages
Date of creation: Jan 2003
Date of revision:
Handle: RePEc:kud:kuiedp:0310

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Article
- Lars Nielsen, 2005. "Monotone risk aversion," Economic Theory, Springer, vol. 25(1), pages 203-215, 01. [Downloadable!] (restricted)
Paper
- Nielsen, Lars Tyge, 1997. "Monotone Risk Aversion," CEPR Discussion Papers 1651, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)

This paper has been announced in the following NEP Reports:

NEP-FIN-2003-07-04 (Finance)
NEP-RMG-2003-07-04 (Risk Management)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Dybvig, Philip H & Lippman, Steven A, 1983. "An Alternative Characterization of Decreasing Absolute Risk Aversion," Econometrica, Econometric Society, vol. 51(1), pages 223-24, January. [Downloadable!] (restricted)
Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October. [Downloadable!] (restricted)

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Frank Hansen, 2007. "Decreasing Relative Risk Premium," Topics in Theoretical Economics, Berkeley Electronic Press, vol. 7(1), pages 1370-1370. [Downloadable!] (restricted)
Frank Hansen, 2006. "Decreasing Relative Risk Premium," Discussion Papers 06-21, University of Copenhagen. Department of Economics. [Downloadable!]

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