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Reduced equivalent form of a financial structure

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  • Aouani, Zaier
  • Cornet, Bernard

Abstract

We consider the two-date model of a financial exchange economy (E,F), with agents’ portfolio restrictions either represented by finitely many linear inequality constraints or satisfying Hart’s (1974) Weak No Market Arbitrage condition. The economy (E,F) is shown to have the same consumption equilibria as a reduced economy (E,F′), for which the set of admissible portfolio allocations is bounded. Building upon the equilibrium existence result for reduced financial economies (E,F′) (Aouani and Cornet, 2009), we then deduce the existence of equilibra of (E,F), under standard assumptions on the consumption side and under the aforementioned assumption on the financial side.

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  • Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:3:p:318-327
    DOI: 10.1016/j.jmateco.2010.12.015
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    Cited by:

    1. Bernard Cornet & Abhishek Ranjan, 2013. "A remark on the set of arbitrage-free prices in a multi-period model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 35-43, March.
    2. Le, Thanh & Le Van, Cuong & Pham, Ngoc-Sang & Sağlam, Çağrı, 2024. "Sperner’s lemma and competitive equilibrium with incomplete financial markets," Economics Letters, Elsevier, vol. 238(C).
    3. Jean-Marc Bonnisseau & Achis Chery, 2014. "On the equivalence of financial structures with long-term assets," Post-Print hal-01130785, HAL.
    4. Sebastián Cea-Echenique & Carlos Hervés-Beloso & Juan Pablo Torres-Martínez, 2017. "Endogenous differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 51-72, January.
    5. Jean-Marc Bonnisseau & Achis Chéry, 2023. "Continuity of marketable payoffs with re-trading," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 31-53, January.
    6. Sebastián Cea-Echenique & Juan Pablo Torres-Martínez, 2018. "General equilibrium with endogenous trading constraints," PLOS ONE, Public Library of Science, vol. 13(9), pages 1-10, September.
    7. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    8. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2016. "Credit segmentation in general equilibrium," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 19-27.
    9. 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.
    10. Sebastián Cea-Echenique & Carlos Hervés-Beloso & Juan Pablo Torres-Martínez, 2012. "Endogenous Information: The Role of Sequential Trade and Financial Participation," Working Papers wp361, University of Chile, Department of Economics.
    11. 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.
    12. Víctor Pérez Fernández & Juan Pablo Torres-Martínez, 2012. "Incomplete Financial Participation: Exclusive Markets, Investment Clubs, and Credit Risk," Working Papers wp363, University of Chile, Department of Economics.
    13. Iraola, Miguel & Torres-Martínez, Juan Pablo, 2013. "Liquidity Contractions, Incomplete Financial Participation and the Prevalence of Negative Equity Non-recourse Loans," MPRA Paper 46838, University Library of Munich, Germany.
    14. Faias Marta & Luque Jaime, 2018. "Cross-listed Securities and Multiple Exchange Memberships: Demand Differentiability and Equilibrium Existence," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-12, January.
    15. Faias, Marta & Torres-Martínez, Juan Pablo, 2017. "Credit market segmentation, essentiality of commodities, and supermodularity," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 115-122.
    16. Maria Bernadette Donato & Monica Milasi & Antonio Villanacci, 2022. "Restricted Participation on Financial Markets: A General Equilibrium Approach Using Variational Inequality Methods," Networks and Spatial Economics, Springer, vol. 22(2), pages 327-359, June.
    17. Iraola, Miguel A. & Sepúlveda, Fabián & Torres-Martínez, Juan Pablo, 2019. "Financial segmentation and collateralized debt in infinite-horizon economies," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 56-69.
    18. A. Jofré & R. T. Rockafellar & R. J-B. Wets, 2017. "General economic equilibrium with financial markets and retainability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 309-345, January.

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    More about this item

    Keywords

    Restricted participation; Portfolio constraints; Financial exchange economy; Reduced financial structure; Equivalent financial structure; Arbitrage-free prices; Consumption equilibrium;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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