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Characterizing useless-free financial structures

Author

Listed:
  • Bernard Cornet

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Zaier Aouani

    (College of Business and Economics, Qatar University - Qatar University)

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.

Suggested Citation

  • Bernard Cornet & Zaier Aouani, 2016. "Characterizing useless-free financial structures," Post-Print halshs-01394836, HAL.
    • Handle: RePEc:hal:journl:halshs-01394836
    DOI: 10.1007/s11228-015-0353-4
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    Cited by:

    1. Alain Chateauneuf & Bernard Cornet, 2022. "Submodular financial markets with frictions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 721-744, April.
    2. Zaier Aouani & Bernard Cornet, 2017. "Eliminating useless portfolios in constrained financial economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 159-190, January.

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