Econometrica: May, 1977, Volume 45, Issue 4

A Matrix Measure of Multivariate Local Risk Aversion

https://doi.org/0012-9682(197705)45:4<895:AMMOML>2.0.CO;2-K
p. 895-904

George T. Duncan

By looking at approximate multivariate risk premiums a matrix measure of multivariate local risk aversion is introduced for a multi-attributed utility function u. This matrix function R(x) = [-u"i"j(x)/u"i(x)] generalizes the univariate measure of Pratt [11] and the conditional measure of Keeney [7]. It has particular advantages in assessing the attitude of a decision-maker toward correlated risks, a concern of Richard [13], and is more informative than the scalar measure proposed by Kihlstrom and Mirman [8]. Simple characteristics of the absolute risk aversion matrix R determine whether a utility function is additive or concave. Assumptions of either constancy or proportionality of R are shown to lead to specific restrictions on the form of u which are more stringent than those of Rothblum [15].