Characterizing Useless-free Financial Structures

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• 作者：Zaier Aouani ; Bernard Cornet
• 关键词：Bounded attainable allocations ; Asymptotic cone ; Useless portfolios ; Redundant assets ; Arbitrage ; free ; 49J53 ; 54C60
• 刊名：Set-Valued and Variational Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：24
• 期：1
• 页码：149-166
• 全文大小：328 KB
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• 作者单位：Zaier Aouani (1)
  Bernard Cornet (2) (3)
  
  1. Department of Economics, Nazarbayev University, Astana, Kazakhstan
  2. University of Kansas, Lawrence, Kansas, USA
  3. Paris School of Economics, Université Paris 1 Panthéon-Sorbonne, Paris, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1877-0541

文摘

The boundedness of the set of admissible allocations is a basic property in economic models that proved to be of fundamental use to show the existence of equilibria (Debreu 1959; Hurwicz and Reiter, Int. Econ. Rev. 14(3), 580–586, 1973). In the study of financial markets without portfolio constraints, this boundedness property is standardly derived from the absence of redundant assets, an assumption that can be made without loss of generality since redundant assets can be eliminated at no cost. However, there are no a priori grounds to do so when agents do face portfolio constraints, and the elimination of redundant assets should be replaced by the elimination of useless portfolios as shown by Aouani and Cornet (2014). The purpose of this paper is thus to characterize financial structures that are useless-free (i.e., without useless portfolios) when agents face portfolio constraints, and show that the absence of useless portfolios adequately extends the absence of redundant assets in the constrained case. Our main result will then show the equivalence between the absence of useless portfolios, a dual non-redundancy property, and the boundedness property of different sets of admissible portfolio allocations. Keywords Bounded attainable allocations Asymptotic cone Useless portfolios Redundant assets Arbitrage-free