Econometrica: May 1977, Volume 45, Issue 4
A Matrix Measure of Multivariate Local Risk Aversion
George T. DuncanBy 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  and the conditional measure of Keeney . It has particular advantages in assessing the attitude of a decision-maker toward correlated risks, a concern of Richard , and is more informative than the scalar measure proposed by Kihlstrom and Mirman . 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 .
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