IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00801402.html
   My bibliography  Save this paper

Equilibria in a multi-period economy

Author

Listed:
  • Bernard Cornet

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - 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)

  • Abhishek Ranjan

    (Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - 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)

Abstract

We consider the model of a financial exchange economy with finitely many periods having financial restricted participation i.e., each agents portfolio choice is restricted to a closed convex set containing zero, as in Siconolfi [1989]. Time and uncertainty are represented by a finite event-tree. There is a market for physical commodities at any state today or in any date of future and financial transfers across time and across states are allowed by means of finitely many financial assets (nominal and numeraire assets). We prove a general existence result of equilibria for such a financial exchange economy in which agents may have non-ordered preferences.

Suggested Citation

  • Bernard Cornet & Abhishek Ranjan, 2013. "Equilibria in a multi-period economy," Post-Print halshs-00801402, HAL.
    • Handle: RePEc:hal:journl:halshs-00801402
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00801402
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00801402/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-880, July.
    3. Magill, Michael & Quinzii, Martine, 1996. "Incomplete markets over an infinite horizon: Long-lived securities and speculative bubbles," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 133-170.
    4. Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103-131.
    5. Alessandro Citanna & Karl Schmedders, 2005. "Excess price volatility and financial innovation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 559-587, October.
    6. Werner, Jan, 1989. "Equilibrium with incomplete markets without ordered preferences," Journal of Economic Theory, Elsevier, vol. 49(2), pages 379-382, December.
    7. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    8. Florenzano, Monique & Gourdel, Pascal & Pascoa, Mario Rui, 2001. "Overlapping generations models with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 36(3), pages 201-218, December.
    9. Florenzano, Monique & Gourdel, Pascal, 1994. "T-period economies with incomplete markets," Economics Letters, Elsevier, vol. 44(1-2), pages 91-97.
    10. Oussama Lachiri & Jean-Marc Bonnisseau, 2004. "Dreze's Criterion In A Multi-Period Economy With Stock Markets," Royal Economic Society Annual Conference 2004 88, Royal Economic Society.
    11. 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.
    12. Monteiro, Paulo Klinger & Pascoa, Mario R., 2000. "Discreteness of equilibria in incomplete markets with a continuum of states," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 229-237, March.
    13. Orrillo, Jaime, 2001. "Default and exogenous collateral in incomplete markets with a continuum of states," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 151-165, February.
    14. 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.
    15. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    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. 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.
    18. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    19. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
    20. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
    21. repec:dau:papers:123456789/6894 is not listed on IDEAS
    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, 2012. "A remark on arbitrage free prices in multi-period economy," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00707401, HAL.

    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. Charalambos Aliprantis & Rabee Tourky, 2009. "Equilibria in incomplete assets economies with infinite dimensional spot markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 221-262, February.
    3. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    4. 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.
    5. Mas-Colell, Andreu & Zame, William R., 1996. "The existence of security market equilibrium with a non-atomic state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 63-84.
    6. Bernard Cornet & Abhishek Ranjan, 2013. "Existence of equilibria via quasi-equilibria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801399, HAL.
    7. 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.
    8. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    9. 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.
    10. 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.
    11. Monique Florenzano, 1999. "General equilibrium of financial markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085543, HAL.
    12. John Geanakoplos & William Zame, 2014. "Collateral equilibrium, I: a basic framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 443-492, August.
    13. Levine, David K., 1989. "Infinite horizon equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 357-376, September.
    14. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research.
    15. Orrilo, Jaime, 2006. "Another Proof of the Existence of GEI Equilibrium with Default and Exogenous Collateral," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(1), May.
    16. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Post-Print halshs-00426399, HAL.
    17. repec:dau:papers:123456789/6894 is not listed on IDEAS
    18. Florenzano, Monique & Gourdel, Pascal, 1994. "T-period economies with incomplete markets," Economics Letters, Elsevier, vol. 44(1-2), pages 91-97.
    19. Emma Moreno-García & Juan Torres-Martínez, 2012. "Equilibrium existence in infinite horizon economies," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 11(2), pages 127-145, August.
    20. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    21. Bosi, Stefano & Van, Cuong Le & Pham, Ngoc-Sang, 2018. "Intertemporal equilibrium with heterogeneous agents, endogenous dividends and collateral constraints," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 1-20.

    More about this item

    Keywords

    arbitrage free prices; equilibrium; financial exchange economy; Multi-period economy; restricted participation; prix sans arbitrage; équilibre général; économie d'échange financière; Multi-période économie; participation contraintes;
    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

    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:hal:journl:halshs-00801402. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.