Title

Arrow-Debreu Equilibria for Rank-Dependent Utilities

Paper

"Jianming Xia and Xun Yu Zhou (2012). Arrow-Debreu Equilibria for Rank-Dependent Utilities. Working Paper"

Abstract

We provide conditions on a one-period-two-date pure exchange economy with rank-dependent utility agents under which Arrow-Debreu equilibria exist. When such an equilibrium exists, we derive the state-price density explicitly, which is a weighted marginal rate of substitution between the initial and the end-of-period consumption of a representative agent, while the weight is expressed through the differential of the probability weighting function.
Based on the result we reach several findings, including that asset prices depend upon agents' subjective beliefs regarding overall consumption growth, that an uncorrelated security's entire probability distribution and its interdependence with the other part of the economy should be priced, and that there is a direction of thinking about the equity premium and risk-free rate puzzles. Moreover, we propose a "rank-neutral probability" as an appropriate modification of the original probability measure under which assets can be priced in the same way as in an economy with expected utility agents.