IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpmi/0503013.html
   My bibliography  Save this paper

Equilibria in exchange economies with financial constraints: Beyond the Cass Trick

Author

Listed:
  • V.F. Martins-da-Rocha

    (CEREMADE)

  • L. Triki

    (CERMSEM)

Abstract

We consider an exchange economy under incomplete financial markets with purely financial securities and finitely many agents. When portfolios are not constrained, Cass (1984), Duffie (1987) and Florenzano--Gourdel (1992) proved that arbitrage-free security prices fully characterize equilibrium security prices. This result is based on a trick initiated by Cass (1984) in which one unconstrained agent behaves as if he were in complete markets. This approach is unsatisfactory since it is asymmetric and no more valid when every agent is subject to frictions. We propose a new and symmetric approach to prove that arbitrage-free security prices still fully characterize equilibrium security prices in the more realistic situation where the financial market is constrained by convex restrictions, provided that financial markets are collectively frictionless.

Suggested Citation

  • 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.
    • Handle: RePEc:wpa:wuwpmi:0503013
    Note: Type of Document - pdf; pages: 18
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/mic/papers/0503/0503013.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Monique Florenzano, 1999. "General equilibrium of financial markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085543, HAL.
    3. Monique Florenzano, 2007. "General equilibrium," Post-Print halshs-00250167, HAL.
    4. Lawrence M. Benveniste & Juan Ketterer, 1992. "Arbitrage Opportunities in Financial Markets are not Inconsistent with Competitive Equilibrium," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 4, pages 45-54, Palgrave Macmillan.
    5. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
    6. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-1467, November.
    7. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
    8. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    9. Rahi, Rohit, 1995. "Partially revealing rational expectations equilibria with nominal assets," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 137-146.
    10. Florenzano, Monique & Gourdel, Pascal, 1994. "T-period economies with incomplete markets," Economics Letters, Elsevier, vol. 44(1-2), pages 91-97.
    11. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    12. 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.
    13. Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
    14. repec:dau:papers:123456789/6894 is not listed on IDEAS
    15. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bernard Cornet & Abhishek Ranjan, 2013. "Equilibria in a multi-period economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801402, HAL.
    2. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    3. 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.
    4. Gori, Michele & Pireddu, Marina & Villanacci, Antonio, 2013. "Regularity and Pareto improving on financial equilibria with price-dependent borrowing restrictions," Research in Economics, Elsevier, vol. 67(1), pages 100-110.
    5. 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.
    6. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    7. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2016. "Credit segmentation in general equilibrium," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 19-27.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    3. repec:dau:papers:123456789/6894 is not listed on IDEAS
    4. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    5. Bernard Cornet & Abhishek Ranjan, 2013. "Equilibria in a multi-period economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801402, HAL.
    6. 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.
    7. Guangsug Hahn & Dong Chul Won, 2007. "Equilibrium in Financial Markets with Market Frictions," Korean Economic Review, Korean Economic Association, vol. 23, pages 267-302.
    8. 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.
    9. Bernard Cornet & Abhishek Ranjan, 2013. "Existence of equilibria via quasi-equilibria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801399, HAL.
    10. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    11. Gourdel & Triki, 2005. "Monetary Policy with Incomplete Markets," Finance 0503026, University Library of Munich, Germany.
    12. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Post-Print halshs-00426399, HAL.
    13. Lionel De Boisdeffre, 2008. "The perfect foresights' assumption revisited: the existence of equilibrium with multiple price expectations," Documents de travail du Centre d'Economie de la Sorbonne b08104, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Pascal Gourdel & Leila Triki, 2005. "Incomplete markets and monetary policy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00193970, HAL.
    15. Abdelkrim Seghir & Leila Triki & Stella Kanellopoulou, 2004. "On the survival and irreducibility assumptions for financial markets with nominal assets," Cahiers de la Maison des Sciences Economiques b04008, Université Panthéon-Sorbonne (Paris 1).
    16. Lionel de Boisdeffre, 2004. "No-arbitrage equilibria with differential information: a proof of existence," Cahiers de la Maison des Sciences Economiques b04035, Université Panthéon-Sorbonne (Paris 1).
    17. Stefano Bosi & Cuong Le Van, 2011. "On the existence of a Ramsey equilibrium with endogenous labor supply and borrowing constraints," Post-Print halshs-00612131, HAL.
    18. Jean-Marc Bonnisseau & Elena Mercato, 2010. "Externalities, consumption constraints and regular economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 123-147, July.
    19. Levine, David K., 1989. "Infinite horizon equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 357-376, September.
    20. Robert Becker & Stefano Bosi & Cuong Van & Thomas Seegmuller, 2015. "On existence and bubbles of Ramsey equilibrium with borrowing constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 329-353, February.
    21. 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.

    More about this item

    Keywords

    Exchange economies; incomplete financial markets; purely financial securities; nominal assets; constrained portfolios; collectively frictionless financial markets; equilibrium security prices; arbitrage-free security prices.;
    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
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpmi:0503013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.