Arrow–Debreu equilibria for rank‐dependent utilities with heterogeneous probability weighting. (1st October 2018)

• Record Type: Journal Article
• Authors: Jin, Hanqing; Xia, Jianming; Zhou, Xun Yu
• Is Part Of: Mathematical finance. Volume 29:Number 3(2019)
• Page Start: 898
• Page End: 927
• Publication Date: 2018-10-01
• Subjects: Arrow–Debreu equilibrium -- comonotone Pareto optimum -- price equilibrium with transfers -- probability weighting -- rank‐dependent utility -- state‐price density -- G11; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12200
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: 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 nonconvex 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.