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On the existence of shadow prices

Author

Listed:
  • Giuseppe Benedetti
  • Luciano Campi
  • Jan Kallsen
  • Johannes Muhle-Karbe

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 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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2013. "On the existence of shadow prices," Finance and Stochastics, Springer, vol. 17(4), pages 801-818, October.
    • Handle: RePEc:spr:finsto:v:17:y:2013:i:4:p:801-818
    DOI: 10.1007/s00780-012-0201-4
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Falkowski, Adrian & Słomiński, Leszek, 2022. "SDEs with two reflecting barriers driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 164-186.
    2. Christoph Czichowsky & Walter Schachermayer, 2015. "Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion," Papers 1505.02416, arXiv.org, revised Aug 2016.
    3. Christoph Czichowsky & Walter Schachermayer, 2014. "Duality Theory for Portfolio Optimisation under Transaction Costs," Papers 1408.5989, arXiv.org.
    4. Czichowsky, Christoph & Schachermayer, Walter & Yang, Junjian, 2017. "Shadow prices for continuous processes," LSE Research Online Documents on Economics 63370, London School of Economics and Political Science, LSE Library.
    5. Christoph Czichowsky & Walter Schachermayer & Junjian Yang, 2014. "Shadow prices for continuous processes," Papers 1408.6065, arXiv.org, revised May 2015.
    6. Czichowsky, Christoph & Schachermayer, Walter, 2016. "Duality theory for portfolio optimisation under transaction costs," LSE Research Online Documents on Economics 63362, London School of Economics and Political Science, LSE Library.
    7. Lingqi Gu & Yiqing Lin & Junjian Yang, 2017. "Utility maximization problem under transaction costs: optimal dual processes and stability," Papers 1710.04363, arXiv.org.
    8. Dmitry Rokhlin, 2013. "On the game interpretation of a shadow price process in utility maximization problems under transaction costs," Finance and Stochastics, Springer, vol. 17(4), pages 819-838, October.
    9. Czichowsky, Christoph & Schachermayer, Walter, 2017. "Portfolio optimisation beyond semimartingales: shadowprices and fractional Brownian motion," LSE Research Online Documents on Economics 67689, London School of Economics and Political Science, LSE Library.
    10. Lingqi Gu & Yiqing Lin & Junjian Yang, 2016. "On the existence of shadow prices for optimal investment with random endowment," Papers 1602.01109, arXiv.org, revised Feb 2017.
    11. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224, arXiv.org, revised Sep 2016.

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    More about this item

    Keywords

    Transaction costs; Shadow prices; Short selling constraints; 91G10; 91B16; G11;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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