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Robust utility maximisation in markets with transaction costs

Author

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  • Huy N. Chau

    (Hungarian Academy of Sciences)

  • Miklós Rásonyi

    (Hungarian Academy of Sciences)

Abstract

We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions, we prove the existence of optimal strategies for investors who maximise their worst-case utility over a class of possible models. We consider utility functions defined on either the positive axis or the whole real line.

Suggested Citation

  • Huy N. Chau & Miklós Rásonyi, 2019. "Robust utility maximisation in markets with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 677-696, July.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:3:d:10.1007_s00780-019-00389-0
    DOI: 10.1007/s00780-019-00389-0
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    References listed on IDEAS

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    1. Anis Matoussi & Dylan Possamaï & Chao Zhou, 2015. "Robust Utility Maximization In Nondominated Models With 2bsde: The Uncertain Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 258-287, April.
    2. Christoph Czichowsky & Walter Schachermayer & Junjian Yang, 2017. "Shadow Prices For Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 623-658, July.
    3. Luciano Campi & Walter Schachermayer, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Finance and Stochastics, Springer, vol. 10(4), pages 579-596, December.
    4. Marcel Nutz, 2016. "Utility Maximization Under Model Uncertainty In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 252-268, April.
    5. Revaz Tevzadze & Teimuraz Toronjadze & Tamaz Uzunashvili, 2013. "Robust utility maximization for a diffusion market model with misspecified coefficients," Finance and Stochastics, Springer, vol. 17(3), pages 535-563, July.
    6. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    7. 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.
    8. repec:dau:papers:123456789/5455 is not listed on IDEAS
    9. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    10. Daniel Bartl, 2016. "Exponential utility maximization under model uncertainty for unbounded endowments," Papers 1610.00999, arXiv.org, revised Feb 2019.
    11. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem For Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 963-987, October.
    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. Ariel Neufeld & Marcel Nutz, 2018. "Robust Utility Maximization With Lã‰Vy Processes," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 82-105, January.
    15. Qian Lin & Frank Riedel, 2014. "Optimal consumption and portfolio choice with ambiguity," Papers 1401.1639, arXiv.org.
    16. Mark P. Owen & Gordan Žitković, 2009. "Optimal Investment With An Unbounded Random Endowment And Utility‐Based Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 129-159, January.
    17. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2017. "Robust Fundamental Theorem for Continuous Processes," Post-Print hal-01076062, HAL.
    18. Ariel Neufeld & Mario Sikic, 2016. "Robust Utility Maximization in Discrete-Time Markets with Friction," Papers 1610.09230, arXiv.org, revised May 2018.
    19. Romain Blanchard & Laurence Carassus, 2018. "Multiple-Priors Optimal Investment In Discrete Time For Unbounded Utility Function," Working Papers hal-01883787, HAL.
    20. Thomas Knispel, 2012. "Asymptotics of robust utility maximization," Papers 1203.1191, arXiv.org.
    21. 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.
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    Citations

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    Cited by:

    1. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2021. "Duality theory for robust utility maximisation," Finance and Stochastics, Springer, vol. 25(3), pages 469-503, July.
    2. Nuerxiati Abudurexiti & Erhan Bayraktar & Takaki Hayashi & Hasanjan Sayit, 2024. "Two-fund separation under hyperbolically distributed returns and concave utility function," Papers 2410.04459, arXiv.org.
    3. Miklós Rásonyi & Andrea Meireles‐Rodrigues, 2021. "On utility maximization under model uncertainty in discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 149-175, January.
    4. Huy N. Chau & Masaaki Fukasawa & Miklós Rásonyi, 2022. "Super‐replication with transaction costs under model uncertainty for continuous processes," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1066-1085, October.
    5. Christoph Czichowsky & Raphael Huwyler, 2022. "Robust utility maximisation under proportional transaction costs for c\`adl\`ag price processes," Papers 2211.00532, arXiv.org, revised Aug 2024.
    6. Ariel Neufeld & Julian Sester & Mario Šikić, 2023. "Markov decision processes under model uncertainty," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 618-665, July.
    7. Huy N. Chau & Masaaki Fukasawa & Miklos Rasonyi, 2021. "Super-replication with transaction costs under model uncertainty for continuous processes," Papers 2102.02298, arXiv.org.

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    More about this item

    Keywords

    Utility maximisation; Transaction cost; Model uncertainty;
    All these keywords.

    JEL classification:

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

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