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A multi-asset investment and consumption problem with transaction costs

Author

Listed:
  • David Hobson

    (University of Warwick)

  • Alex S. L. Tse

    (Imperial College London)

  • Yeqi Zhu

    (Credit Suisse)

Abstract

In this article, we study a multi-asset version of the Merton investment and consumption problem with CRRA utility and proportional transaction costs. We specialise to a case where transaction costs are zero except for sales and purchases of a single asset which we call the illiquid asset. We show that the underlying HJB equation can be transformed into a boundary value problem for a first order differential equation. Important properties of the multi-asset problem (including when the problem is well-posed, ill-posed, or well-posed for some values of transaction costs only) can be inferred from the behaviours of a quadratic function of a single variable and another algebraic function.

Suggested Citation

  • David Hobson & Alex S. L. Tse & Yeqi Zhu, 2019. "A multi-asset investment and consumption problem with transaction costs," Finance and Stochastics, Springer, vol. 23(3), pages 641-676, July.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:3:d:10.1007_s00780-019-00391-6
    DOI: 10.1007/s00780-019-00391-6
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    References listed on IDEAS

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    Cited by:

    1. Martin Herdegen & David Hobson & Alex S. L. Tse, 2024. "Portfolio Optimization under Transaction Costs with Recursive Preferences," Papers 2402.08387, arXiv.org.
    2. Baojun Bian & Xinfu Chen & Min Dai & Shuaijie Qian, 2021. "Penalty method for portfolio selection with capital gains tax," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 1013-1055, July.
    3. Jin Hyuk Choi & Tae Ung Gang, 2021. "Optimal investment in illiquid market with search frictions and transaction costs," Papers 2101.09936, arXiv.org, revised Aug 2021.
    4. Alex S. L. Tse & Harry Zheng, 2023. "Speculative trading, prospect theory and transaction costs," Finance and Stochastics, Springer, vol. 27(1), pages 49-96, January.

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    More about this item

    Keywords

    Portfolio choice; Transaction costs; Multiple assets; Hamilton–Jacobi–Bellman equation; Free boundary value problem;
    All these keywords.

    JEL classification:

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

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