Citation

Discussion Paper Details

Please find the details for DP1651 in an easy to copy and paste format below:

Full Details   |   Bibliographic Reference

Full Details

Title: Monotone Risk Aversion

Author(s): Lars Tyge Nielsen

Publication Date: May 1997

Keyword(s): Decreasing Absolute Risk Aversion and Risk Aversion

Programme Area(s): Financial Economics

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.

For full details and related downloads, please visit: https://cepr.org/active/publications/discussion_papers/dp.php?dpno=1651

Bibliographic Reference

Nielsen, L. 1997. 'Monotone Risk Aversion'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=1651