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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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    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. Geanakoplos, John & Shafer, Wayne, 1990. "Solving systems of simultaneous equations in economics," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 69-93.
    4. Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67.
    5. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Post-Print halshs-03330770, HAL.
    6. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Post-Print halshs-00426399, HAL.
    7. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    8. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    9. Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106.
    10. Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
    11. Seghir, Abdelkrim & Torres-Martínez, Juan Pablo, 2011. "On equilibrium existence with endogenous restricted financial participation," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 37-42, January.
    12. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    13. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    14. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Post-Print halshs-01394846, HAL.
    15. V.F. Martins-da-Rocha & L. Triki, 2005. "Equilibria in exchange economies with financial constraints: Beyond the Cass Trick," Microeconomics 0503013, University Library of Munich, Germany.
    16. Cass, David & Siconolfi, Paolo & Villanacci, Antonio, 2001. "Generic regularity of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 61-76, September.
    17. Carosi, Laura & Gori, Michele & Villanacci, Antonio, 2009. "Endogenous restricted participation in general financial equilibrium," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 787-806, December.
    18. Duffie, Darrell & Shafer, Wayne, 1986. "Equilibrium in incomplete markets: II : Generic existence in stochastic economies," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 199-216, June.
    19. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
    20. Jean-Marc Bonnisseau & Bernard Cornet, 2006. "Existence of equilibria with a tight marginal," Cahiers de la Maison des Sciences Economiques b06022, Université Panthéon-Sorbonne (Paris 1).
    21. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
    22. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    23. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    24. Polemarchakis, H. M. & Siconolfi, P., 1997. "Generic existence of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 289-311, October.
    25. Balasko, Yves & Cass, David & Siconolfi, Paolo, 1990. "The structure of financial equilibrium with exogenous yields : The case of restricted participation," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 195-216.
    26. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03330770, HAL.
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    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. Jean-Marc Bonnisseau & Achis Chery, 2014. "On the equivalence of financial structures with long-term assets," Documents de travail du Centre d'Economie de la Sorbonne 14081, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2016. "Credit segmentation in general equilibrium," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 19-27.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Miguel A. Iraola & Juan Pablo Torres-Martinez, 2013. "Liquidity Contractions, Incomplete Financial Participation and the Prevalence of Negative Equity Non-Recourse Loans," Working Papers 2013-08, University of Miami, Department of Economics.
    15. 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.
    16. 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.
    17. 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.
    18. 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.

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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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