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Arrow-Debreu equilibria for rank-dependent utilities with heterogeneous probability weighting
Jin, Hanqing1,2; Xia, Jianming3; Zhou, Xun Yu4
2019-07-01
Source PublicationMATHEMATICAL FINANCE
ISSN0960-1627
Volume29Issue:3Pages:898-927
AbstractWe 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.
KeywordArrow-Debreu equilibrium comonotone Pareto optimum price equilibrium with transfers probability weighting rank-dependent utility state-price density G11
DOI10.1111/mafi.12200
Language英语
Funding ProjectNSFC (National Natural Science Foundation of China)[11231005] ; Columbia University ; Oxford-Man Institute of Quantitative Finance ; Oxford-Nie Financial Big Data Lab
WOS Research AreaBusiness & Economics ; Mathematics ; Mathematical Methods In Social Sciences
WOS SubjectBusiness, Finance ; Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods
WOS IDWOS:000470926900008
PublisherWILEY
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34988
Collection应用数学研究所
Corresponding AuthorZhou, Xun Yu
Affiliation1.Univ Oxford, Math Inst, Oxford, England
2.Univ Oxford, Oxford Nie Financial Big Data Lab, Oxford, England
3.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, NCMIS, Beijing, Peoples R China
4.Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA
Recommended Citation
GB/T 7714
Jin, Hanqing,Xia, Jianming,Zhou, Xun Yu. Arrow-Debreu equilibria for rank-dependent utilities with heterogeneous probability weighting[J]. MATHEMATICAL FINANCE,2019,29(3):898-927.
APA Jin, Hanqing,Xia, Jianming,&Zhou, Xun Yu.(2019).Arrow-Debreu equilibria for rank-dependent utilities with heterogeneous probability weighting.MATHEMATICAL FINANCE,29(3),898-927.
MLA Jin, Hanqing,et al."Arrow-Debreu equilibria for rank-dependent utilities with heterogeneous probability weighting".MATHEMATICAL FINANCE 29.3(2019):898-927.
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