Econometrica Vol. 45 No. 4 1977
A Matrix Measure of Multivariate Local Risk Aversion
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) = [-uij(x)/ui(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].
- DOI
- 10.2307/1912680
- Volume
- 45
- Issue
- 4
- Pages
- 895
- Sources
- bibtex:phds-export.bib openalex crossref