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On the rank of payoff matrices with long-term assets

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  • Jean-Marc Bonnisseau

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

  • Achis Chery

    () (Université Quisqueya - Faculté des Sciences, de Génie et d'Architecture (FSGA), CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne)

Abstract

We consider a stochastic financial exchange economy with a finite date-event tree representing time and uncertainty and a nominal financial structure with possibly long-term assets. We exhibit a sufficient condition under which the payoff matrix and the full payoff matrix have the same rank. This generalizes previous results of Angeloni-Cornet and Magill-Quinzii involving only short-term assets. We then derive existence results with assumptions only based on the fundamentals of the economy.

Suggested Citation

  • Jean-Marc Bonnisseau & Achis Chery, 2011. "On the rank of payoff matrices with long-term assets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00659183, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00659183
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00659183
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    References listed on IDEAS

    as
    1. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    2. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 227-252, October.
    3. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
    4. Laura Angeloni & Bernard Cornet, 2005. "Existence Of Financial Equilibria In A Multiperiod Stochastic Economy," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200506, University of Kansas, Department of Economics, revised Feb 2005.
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    Keywords

    long-term assets; Marchés incomplets; équilibre financier; modèle à plusieurs périodes; actifs de long terme.; Incomplete markets; financial equilibrium; multi-period model; long-term assets.;

    JEL classification:

    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • G1 - Financial Economics - - General Financial Markets

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