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Anything is Possible: On the Existence and Uniqueness of Equilibria in the Shleifer-Vishny Model of Limits of Arbitrage

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  • Arnold, Lutz G.

Abstract

This paper gives a complete characterization of the equilibria in Shleifer and Vishny's (1997) model of "Limits of Arbitrage". We show that expected wealth (the arbitrageurs' objective function) is a possibly non-concave function of investment and that the relation between investment and prices is not necessarily continuous or single-valued or well-defined. As a result, "anything is possible": non-existence or multiplicity of equilibria may arise, and sunspots may govern the equilibrium selection in the latter case. Es wird eine vollständige Charakterisierung möglicher Gleichgewichte im Shleifer-Vishny-Modell zu Grenzen der Arbitrage vorgenommen. Zunächst wird gezeigt, dass die Zielfunktion der Arbitrageure - ihr erwartetes Vermögen - eine nicht-konkave Funktion ihrer Investitionen ist und dass die Abbildung, die die aggregierten Investitionen und die Vermögenspreise in Beziehung zueinander setzt, möglicherweise unstetig, mehrwertig oder gar nicht wohldefiniert ist. Als Konsequenz hieraus "ist alles möglich": Nicht-Existenz eines Gleichgewichts ebenso wie Multiplizität. Im zweiten Fall können Sonnenflecken die Gleichgewichtsauswahl bestimmen.

Suggested Citation

  • Arnold, Lutz G., 2009. "Anything is Possible: On the Existence and Uniqueness of Equilibria in the Shleifer-Vishny Model of Limits of Arbitrage," University of Regensburg Working Papers in Business, Economics and Management Information Systems 13, University of Regensburg, Department of Economics.
    • Handle: RePEc:bay:rdwiwi:15563
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    1. Shleifer, Andrei & Vishny, Robert W, 1997. "The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
    2. Barberis, Nicholas & Thaler, Richard, 2003. "A survey of behavioral finance," 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 18, pages 1053-1128, Elsevier.
    3. Glaser, Markus & Nöth, Markus & Weber, Martin, 2003. "Behavioral Finance," Sonderforschungsbereich 504 Publications 03-14, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
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    2. Wang, Wenzhao & Su, Chen & Duxbury, Darren, 2022. "The conditional impact of investor sentiment in global stock markets: A two-channel examination," Journal of Banking & Finance, Elsevier, vol. 138(C).
    3. Arnold, Lutz G. & Brunner, Stephan, 2015. "The economics of rational speculation in the presence of positive feedback trading," The Quarterly Review of Economics and Finance, Elsevier, vol. 57(C), pages 161-174.
    4. Lutz G. Arnold & Stephan Brunner, 2012. "Is Rational Speculation in the Presence of Positive Feedback Traders Destabilizing?," Working Papers 119, Bavarian Graduate Program in Economics (BGPE).

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