We study the representative consumer's risk attitude and efficient risk-sharing rules in a single-period, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must...

In this paper, we first present a unified characterization of downside risk aversion measures, using a popular approach in the literature. In the process, we make the following contribution: we characterize the two downside risk aversion measures cautiousness and the ratio of a utility...