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A Matrix Measure of Multivariate Local Risk Aversion

George T. Duncan
Econometrica
Vol. 45, No. 4 (May, 1977), pp. 895-903
Published by: The Econometric Society
DOI: 10.2307/1912680
Stable URL: http://www.jstor.org/stable/1912680
Page Count: 9
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A Matrix Measure of Multivariate Local Risk Aversion
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Abstract

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].

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