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On the market viability under proportional transaction costs

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  • Erhan Bayraktar
  • Xiang Yu

Abstract

This paper studies the market viability with proportional transaction costs. Instead of requiring the existence of strictly consistent price systems as in the literature, we show that strictly consistent local martingale systems (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABPs). In particular, we show that the NUPBR and NLABP conditions in the robust sense are equivalent to the existence of SCLMS for general market models. We also discuss the implications for the utility maximization problem.

Suggested Citation

  • Erhan Bayraktar & Xiang Yu, 2018. "On the market viability under proportional transaction costs," Mathematical Finance, Wiley Blackwell, vol. 28(3), pages 800-838, July.
    • Handle: RePEc:bla:mathfi:v:28:y:2018:i:3:p:800-838
    DOI: 10.1111/mafi.12155
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    Cited by:

    1. Christoph Czichowsky & Rémi Peyre & Walter Schachermayer & Junjian Yang, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Post-Print hal-02373296, HAL.
    2. Christoph Kuhn, 2023. "The fundamental theorem of asset pricing with and without transaction costs," Papers 2307.00571, arXiv.org, revised Aug 2024.
    3. Erhan Bayraktar & Leonid Dolinskyi & Yan Dolinsky, 2020. "Extended weak convergence and utility maximisation with proportional transaction costs," Finance and Stochastics, Springer, vol. 24(4), pages 1013-1034, October.
    4. Christoph Kuhn & Alexander Molitor, 2020. "Semimartingale price systems in models with transaction costs beyond efficient friction," Papers 2001.03190, arXiv.org, revised Aug 2021.
    5. Czichowsky, Christoph Johannes & Peyre, Rémi & Schachermayer, Walter & Yang, Junjian, 2018. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," LSE Research Online Documents on Economics 85230, London School of Economics and Political Science, LSE Library.
    6. 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.
    7. Francesca Biagini & Thomas Reitsam, 2019. "Asset Price Bubbles in market models with proportional transaction costs," Papers 1911.10149, arXiv.org, revised Dec 2020.
    8. 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.
    9. Christoph Czichowsky & R'emi Peyre & Walter Schachermayer & Junjian Yang, 2016. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Papers 1608.01415, arXiv.org.
    10. 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.

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