Characterizing Useless-free Financial Structures

Zaier Aouani, Bernard Cornet

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)149-166
Number of pages18
JournalSet-Valued and Variational Analysis
Volume24
Issue number1
DOIs
Publication statusPublished - Mar 1 2016

Keywords

  • Arbitrage-free
  • Asymptotic cone
  • Bounded attainable allocations
  • Redundant assets
  • Useless portfolios

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Geometry and Topology
  • Numerical Analysis
  • Statistics and Probability

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