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...

The Black-Scholesmodelis basedona one-parameter pricingkernel with constantelasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel withat leasttwo parameters.We price European-style optionson assets whose probability distributions have two unknown...

We define two new stochastic orders combining probability ratio and likelihood ratio and specify two respective classes of payoff functions, which nest most models in the literature as special cases, such that a risk change satisfies one of the two stochastic orders if and only if given any...