KMS Of Academy of mathematics and systems sciences, CAS
Arrow-Debreu equilibria for rank-dependent utilities with heterogeneous probability weighting | |
Jin, Hanqing1,2; Xia, Jianming3; Zhou, Xun Yu4 | |
2019-07-01 | |
Source Publication | MATHEMATICAL FINANCE |
ISSN | 0960-1627 |
Volume | 29Issue:3Pages:898-927 |
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. |
Keyword | Arrow-Debreu equilibrium comonotone Pareto optimum price equilibrium with transfers probability weighting rank-dependent utility state-price density G11 |
DOI | 10.1111/mafi.12200 |
Language | 英语 |
Funding Project | NSFC (National Natural Science Foundation of China)[11231005] ; Columbia University ; Oxford-Man Institute of Quantitative Finance ; Oxford-Nie Financial Big Data Lab |
WOS Research Area | Business & Economics ; Mathematics ; Mathematical Methods In Social Sciences |
WOS Subject | Business, Finance ; Economics ; Mathematics, Interdisciplinary Applications ; Social Sciences, Mathematical Methods |
WOS ID | WOS:000470926900008 |
Publisher | WILEY |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/34988 |
Collection | 应用数学研究所 |
Corresponding Author | Zhou, Xun Yu |
Affiliation | 1.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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