[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/16062.html
   My bibliography  Save this paper

Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities

Author

Abstract
We consider a model with an infinite number of states of nature, von Neumann - Morgenstern utilities, where agents have different probability beliefs and where short sells are allowed. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. However, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold

Suggested Citation

  • Thai Ha-Huy & Cuong Le Van & Nguyen Manh-Hung, 2016. "Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities," Documents de travail du Centre d'Economie de la Sorbonne 16062, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:16062
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2016/16062.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Donald J. Brown & Jan Werner, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 101-114.
    2. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," PSE-Ecole d'économie de Paris (Postprint) halshs-00308530, HAL.
    3. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 373-391, December.
    4. Dana, R. A. & Le Van, C., 1996. "Asset Equilibria in Lp spaces with complete markets: A duality approach," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 263-280.
    5. Wassim Daher & V. Martins-da-Rocha & Yiannis Vailakis, 2007. "Asset market equilibrium with short-selling and differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 425-446, September.
    6. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 153-162, August.
    7. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December.
    8. Geistdoerfer-Florenzano, Monique, 1982. "The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 113-134, January.
    9. Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
    10. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, vol. 87(1), pages 169-193, July.
    11. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
    12. repec:dau:papers:123456789/5045 is not listed on IDEAS
    13. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," PSE-Ecole d'économie de Paris (Postprint) halshs-00470670, HAL.
    14. Rose-Anne Dana & Cuong Le Van, 2007. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00188761, HAL.
    15. Le Van, Cuong, 1996. "Complete Characterization of Yannelis-Zame and Chichilnisky-Kalman-Mas-Colell Properness Conditions on Preferences for Separable Concave Functions Defined in L[superscript p subscript +] and L[supersc," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 155-166, June.
    16. Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 137-152.
    17. Won, Dong Chul & Yannelis, Nicholas C., 2008. "Equilibrium theory with unbounded consumption sets and non-ordered preferences: Part I. Non-satiation," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1266-1283, December.
    18. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    19. Chichilnisky Graciela & Heal Geoffrey M., 1993. "Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales," Journal of Economic Theory, Elsevier, vol. 59(2), pages 364-384, April.
    20. 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.
    21. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Post-Print halshs-00470670, HAL.
    22. Le Van, Cuong & Truong Xuan, Duc Ha, 2001. "Asset market equilibrium in Lp spaces with separable utilities," Journal of Mathematical Economics, Elsevier, vol. 36(3), pages 241-254, December.
    23. repec:dau:papers:123456789/2967 is not listed on IDEAS
    24. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Post-Print halshs-00308530, HAL.
    25. repec:dau:papers:123456789/2342 is not listed on IDEAS
    26. Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 467-473.
    27. repec:dau:papers:123456789/6228 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. Ha-Huy, Thai & Le Van, Cuong, 2017. "Existence of equilibrium on asset markets with a countably infinite number of states," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 44-53.
    2. Thai Ha-Huy & Cuong Le Van, 2012. "Asset market equilibrium with short-selling and a continuum of number of states of nature," Working Papers hal-04132780, 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. Ha-Huy, Thai & Le Van, Cuong, 2017. "Existence of equilibrium on asset markets with a countably infinite number of states," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 44-53.
    2. Thai Ha Huy & Cuong Le Van, 2014. "Arbitrage and asset market equilibrium in finite dimensional economies with short," Working Papers 2014-122, Department of Research, Ipag Business School.
    3. Ha-Huy, Thai & Le Van, Cuong & Tran-Viet, Cuong, 2018. "Arbitrage and equilibrium in economies with short-selling and ambiguity," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 95-100.
    4. Thai Ha-Huy & Cuong Le Van & Frank Page & Myrna Wooders, 2017. "No-arbitrage and Equilibrium in Finite Dimension: A General Result," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01529663, HAL.
    5. Thai Ha-Huy & Cuong Le Van & Myrna Wooders, 2024. "Existence of Equilibrium in Finite Dimensional Asset Markets," Working Papers hal-04131008, HAL.
    6. Thai Ha-Huy & Cuong Le Van, 2012. "Asset market equilibrium with short-selling and a continuum of number of states of nature," Working Papers hal-04132780, HAL.
    7. Ha-Huy, Thai & Le Van, Cuong & Nguyen, Manh-Hung, 2011. "Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities," LERNA Working Papers 11.12.346, LERNA, University of Toulouse.
    8. Dana, R.A. & Le Van, C., 2014. "Efficient allocations and equilibria with short-selling and incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 101-105.
    9. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 353-370, January.
    10. Stefano Bosi & Patrice Fontaine & Cuong Le Van, 2013. "Equilibrium existence in the international asset and good markets," Working Papers 2013-3, Department of Research, Ipag Business School.
    11. Wassim Daher & V. Martins-da-Rocha & Yiannis Vailakis, 2007. "Asset market equilibrium with short-selling and differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 425-446, September.
    12. Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
    13. Le Van, Cuong & Truong Xuan, Duc Ha, 2001. "Asset market equilibrium in Lp spaces with separable utilities," Journal of Mathematical Economics, Elsevier, vol. 36(3), pages 241-254, December.
    14. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, August.
    15. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.
    16. Allouch, Nizar & Van, Cuong Le & Page Jr. Frank H., 2002. "Arbitrage, Equilibrium And Nonsatiation," The Warwick Economics Research Paper Series (TWERPS) 637, University of Warwick, Department of Economics.
    17. repec:ipg:wpaper:2013-003 is not listed on IDEAS
    18. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2006. "Arbitrage and equilibrium in unbounded exchange economies with satiation," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 661-674, September.
    19. Patrick Cheridito & Ulrich Horst & Michael Kupper & Traian A. Pirvu, 2016. "Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 174-195, February.
    20. Martins-da-Rocha, V. Filipe & Monteiro, Paulo K., 2009. "Unbounded exchange economies with satiation: How far can we go?," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 465-478, July.
    21. Tim J. Boonen & Fangda Liu & Ruodu Wang, 2021. "Competitive equilibria in a comonotone market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1217-1255, November.

    More about this item

    Keywords

    asset market equilibrium; individually rational attainable allocations; individually rational utility set; no-arbitrage prices; no-arbitrage condition;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G1 - Financial Economics - - General Financial Markets

    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:mse:cesdoc:16062. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    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.