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On the existence of shadow prices

  • 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).)

Registered author(s):

    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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    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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    1. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165.
    2. Luciano Campi & Mark Owen, 2011. "Multivariate utility maximization with proportional transaction costs," Finance and Stochastics, Springer, vol. 15(3), pages 461-499, September.
    3. HuyËn Pham & Nizar Touzi & Jaksa Cvitanic, 1999. "A closed-form solution to the problem of super-replication under transaction costs," Finance and Stochastics, Springer, vol. 3(1), pages 35-54.
    4. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
    5. Cvitanic, Jaksa & Wang, Hui, 2001. "On optimal terminal wealth under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 223-231, April.
    6. Bouchard, Bruno, 2002. "Utility Maximization on the Real Line under Proportional Transaction Costs," Economics Papers from University Paris Dauphine 123456789/1532, Paris Dauphine University.
    7. 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.
    8. 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.
    9. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    10. repec:fth:inseep:9513 is not listed on IDEAS
    11. Giuseppe Benedetti & Luciano Campi, 2011. "Multivariate utility maximization with proportional transaction costs and random endowment," Working Papers hal-00586377, HAL.
    12. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    13. Paolo Guasoni & Mikl\'os R\'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    14. 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.
    15. Bruno Bouchard, 2002. "Utility maximization on the real line under proportional transaction costs," Finance and Stochastics, Springer, vol. 6(4), pages 495-516.
    16. 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.
    17. Owen, Mark & Campi, Luciano, 2011. "Multivariate Utility Maximization with Proportional Transaction Costs," Economics Papers from University Paris Dauphine 123456789/2318, Paris Dauphine University.
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