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On the existence of shadow prices

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Author Info

  • Giuseppe Benedetti

    (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

  • Luciano Campi

    ()
    (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, LAGA - Laboratoire d'Analyse, Géométrie et Applications - CNRS : UMR7539 - Université Paris-Nord - Paris XIII)

  • Jan Kallsen

    (mathematisches seminar - Christian-Albrechts-Universität zu Kiel)

  • Johannes Muhle-Karbe

    (Mathematics Department - Swiss Federal Institute of Technology in Zurich (ETH Zurich).)

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    Abstract

    For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless {\em shadow market} that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample which shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid-ask-spreads.

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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00645980.

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    Date of creation: 28 Nov 2011
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    Handle: RePEc:hal:wpaper:hal-00645980

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00645980/en/
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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Owen, Mark & Campi, Luciano, 2011. "Multivariate Utility Maximization with Proportional Transaction Costs," Economics Papers from University Paris Dauphine 123456789/2318, Paris Dauphine University.
    2. Lamberton, Damien & Pham, Huyên & Schweizer, Martin, 1998. "Local risk-minimization under transaction costs," SFB 373 Discussion Papers 1998,18, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. Bruno Bouchard, 2002. "Utility maximization on the real line under proportional transaction costs," Finance and Stochastics, Springer, Springer, vol. 6(4), pages 495-516.
    4. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(2), pages 133-165.
    5. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 89(1), pages 31-48, September.
    6. Loewenstein, Mark, 2000. "On optimal portfolio trading strategies for an investor facing transactions costs in a continuous trading market," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 209-228, March.
    7. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    8. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, Springer, vol. 3(2), pages 237-248.
    9. HuyËn Pham & Nizar Touzi & Jaksa Cvitanic, 1999. "A closed-form solution to the problem of super-replication under transaction costs," Finance and Stochastics, Springer, Springer, vol. 3(1), pages 35-54.
    10. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
    11. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, Elsevier, vol. 66(1), pages 178-197, June.
    12. repec:fth:inseep:9513 is not listed on IDEAS
    13. Bouchard, Bruno, 2002. "Utility Maximization on the Real Line under Proportional Transaction Costs," Economics Papers from University Paris Dauphine 123456789/1532, Paris Dauphine University.
    14. Giuseppe Benedetti & Luciano Campi, 2011. "Multivariate utility maximization with proportional transaction costs and random endowment," Working Papers hal-00586377, HAL.
    15. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.
    16. Luciano Campi & Mark Owen, 2011. "Multivariate utility maximization with proportional transaction costs," Finance and Stochastics, Springer, Springer, vol. 15(3), pages 461-499, September.
    17. repec:wop:humbsf:1998-18 is not listed on IDEAS
    18. Cvitanic, Jaksa & Wang, Hui, 2001. "On optimal terminal wealth under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 223-231, April.
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    Cited by:
    1. Christoph Czichowsky & Johannes Muhle-Karbe & Walter Schachermayer, 2012. "Transaction Costs, Shadow Prices, and Duality in Discrete Time," Papers 1205.4643, arXiv.org, revised Jan 2014.
    2. Johannes Muhle-Karbe & Ren Liu, 2012. "Portfolio Selection with Small Transaction Costs and Binding Portfolio Constraints," Papers 1205.4588, arXiv.org, revised Jan 2013.

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