Arrow-Debreu Equilibria for Rank-Dependent Utilities

45 Pages Posted: 15 Sep 2012

See all articles by Jianming Xia

Jianming Xia

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Multiple version iconThere are 2 versions of this paper

Date Written: September 14, 2012

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.

Keywords: Rank-dependent utility, probability weighting, Arrow-Debreu Equilibrium, state-price density

JEL Classification: G11, G12

Suggested Citation

Xia, Jianming and Zhou, Xunyu, Arrow-Debreu Equilibria for Rank-Dependent Utilities (September 14, 2012). Available at SSRN: https://ssrn.com/abstract=2146353 or http://dx.doi.org/10.2139/ssrn.2146353

Jianming Xia (Contact Author)

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences ( email )

Zhong-Guan-Cun-Dong-Lu 55, Haidian District
Beijing 100190
China

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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