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Asymptotics for fixed transaction costs

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  • Albert Altarovici
  • Johannes Muhle-Karbe
  • Halil Soner

Abstract

An investor with constant relative risk aversion trades a safe and several risky assets with constant investment opportunities. For a small fixed transaction cost, levied on each trade regardless of its size, we explicitly determine the leading-order corrections to the frictionless value function and optimal policy. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Albert Altarovici & Johannes Muhle-Karbe & Halil Soner, 2015. "Asymptotics for fixed transaction costs," Finance and Stochastics, Springer, vol. 19(2), pages 363-414, April.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:2:p:363-414
    DOI: 10.1007/s00780-015-0261-3
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Cohen, Samuel N. & Henckel, Timo & Menzies, Gordon D. & Muhle-Karbe, Johannes & Zizzo, Daniel J., 2019. "Switching cost models as hypothesis tests," Economics Letters, Elsevier, vol. 175(C), pages 32-35.
    2. Christoph Belak & Lukas Mich & Frank T. Seifried, 2022. "Optimal investment for retail investors," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 555-594, April.
    3. Alain Bensoussan & Guiyuan Ma & Chi Chung Siu & Sheung Chi Phillip Yam, 2022. "Dynamic mean–variance problem with frictions," Finance and Stochastics, Springer, vol. 26(2), pages 267-300, April.
    4. Kasper Larsen & Oleksii Mostovyi & Gordan Žitković, 2018. "An expansion in the model space in the context of utility maximization," Finance and Stochastics, Springer, vol. 22(2), pages 297-326, April.
    5. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672, arXiv.org, revised Apr 2020.
    6. Yaroslav Melnyk & Frank Thomas Seifried, 2018. "Small†cost asymptotics for long†term growth rates in incomplete markets," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 668-711, April.
    7. Eberhard Mayerhofer, 2024. "Asymptotic Methods for Transaction Costs," Risks, MDPI, vol. 12(4), pages 1-32, April.
    8. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    9. Christoph Belak & Lukas Mich & Frank T. Seifried, 2019. "Optimal Investment for Retail Investors with Flooredand Capped Costs," Working Paper Series 2019-06, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    10. Soren Christensen & Albrecht Irle & Andreas Ludwig, 2016. "Optimal portfolio selection under vanishing fixed transaction costs," Papers 1611.01280, arXiv.org, revised Jul 2017.
    11. Ibrahim Ekren & Ren Liu & Johannes Muhle-Karbe, 2015. "Optimal Rebalancing Frequencies for Multidimensional Portfolios," Papers 1510.05097, arXiv.org, revised Sep 2017.
    12. Mogens Graf Plessen & Alberto Bemporad, 2017. "A posteriori multi-stage optimal trading under transaction costs and a diversification constraint," Papers 1709.07527, arXiv.org, revised Apr 2018.
    13. Albert Altarovici & Max Reppen & H. Mete Soner, 2016. "Optimal Consumption and Investment with Fixed and Proportional Transaction Costs," Papers 1610.03958, arXiv.org.
    14. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    15. Christoph Belak & Sören Christensen, 2019. "Utility maximisation in a factor model with constant and proportional transaction costs," Finance and Stochastics, Springer, vol. 23(1), pages 29-96, January.
    16. Yingting Miao & Qiang Zhang, 2023. "Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility," Papers 2304.07672, arXiv.org.
    17. Xinfu Chen & Min Dai & Wei Jiang & Cong Qin, 2022. "Asymptotic analysis of long‐term investment with two illiquid and correlated assets," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1133-1169, October.

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    More about this item

    Keywords

    Fixed transaction costs; Optimal investment and consumption; Homogenization; Viscosity solutions; Asymptotic expansions; 91G10; 91G80; 35K55; 60H30; G11;
    All these keywords.

    JEL classification:

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

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