Arrow-Debreu Equilibria for Rank-Dependent Utilities with Heterogeneous Probability Weighting
Forthcoming, Mathematical Finance
36 Pages Posted: 21 Aug 2018
Date Written: August 8, 2018
We study Arrow-Debreu equilibria for a one-period-two-date pure exchange economy with rank-dependent utility agents having heterogeneous probability weighting and outcome utility functions. In particular, we allow the economy to have a mix of expected utility agents and rank-dependent utility ones, with non-convex probability weighting functions. The standard approach for convex economy equilibria fails due to the incompatibility with second-order stochastic dominance. The representative agent approach devised in Xia and Zhou (2016) does not work either due to the heterogeneity of the weighting functions. We overcome these difficulties by considering the comonotone allocations, on which the rank-dependent utilities become concave. Accordingly, we introduce the notion of comonotone Pareto optima, and derive their characterizing conditions. With the aid of the auxiliary problem of price equilibria with transfers, we provide a sufficient condition in terms of the model primitives under which an Arrow-Debreu equilibrium exists, along with the explicit expression of the state-price density in equilibrium. This new, general sufficient condition distinguishes the paper from previous related studies with homogeneous and/or convex probability weightings.
Keywords: rank-dependent utility, probability weighting, Arrow-Debreu equilibrium, state-price density, comonotone Pareto optimum, price equilibrium with transfers
JEL Classification: G11
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