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 propose a new downside risk aversion measure, which is called cautiousness in the literature. Using a simple portfolio problem with a risk-free bond, a stock, and an option on the stock, we show that, an agent has higher cautiousness (i) if and only if she is always more likely...

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...

When is it appropriate to add a convex component such as stock options to an optimal, managerial compensation contract? We show that, contrary to what is said in the literature, it is not risk aversion but cautiousness, a downside risk aversion measure, which gives the answer. When stockholders...