Abstract
In this note we extend the theory of precautionary saving to the case of multivariate risk. We introduce
a notion of multivariate prudence, related to a precautionary premium, and we propose a matrix-measure
to capture the strength of the precautionary saving motive. We discuss the usefulness of this measure,
in particular for comparing precautionary behavior among individuals. We also characterize the notion of
multivariate downside risk aversion as a preference for disaggregating harms across outcomes of multivariate
lotteries. We show the link between this notion and the notion of multivariate prudence, we propose
a matrix-measure of its intensity, and we illustrate the usefulness of our results in a problem of social
discounting.