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Extended weak convergence and utility maximisation with proportional transaction costs

Author

Listed:
  • Erhan Bayraktar

    (University of Michigan)

  • Leonid Dolinskyi

    (The University of the State Fiscal Service)

  • Yan Dolinsky

    (Hebrew University)

Abstract

In this paper, we study utility maximisation with proportional transaction costs. Assuming extended weak convergence of the underlying processes, we prove the convergence of the time-0 values of the corresponding utility maximisation problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in Aldous (Weak Convergence of Stochastic Processes for Processes Viewed in the Strasbourg Manner, 1981) and on the Meyer–Zheng topology introduced in Meyer and Zheng (Ann. Inst. Henri Poincaré Probab. Stat. 20:353–372, 1984).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:4:d:10.1007_s00780-020-00437-0
    DOI: 10.1007/s00780-020-00437-0
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. David M. Kreps & Walter Schachermayer, 2020. "Convergence of optimal expected utility for a sequence of discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1205-1228, October.
    2. Muqiao Huang & Ruodu Wang, 2024. "Coherent risk measures and uniform integrability," Papers 2404.03783, arXiv.org, revised Oct 2024.
    3. Tae Ung Gang & Jin Hyuk Choi, 2024. "Unified Asymptotics For Investment Under Illiquidity: Transaction Costs And Search Frictions," Papers 2407.13547, arXiv.org.
    4. Erhan Bayraktar & Christoph Czichowsky & Leonid Dolinskyi & Yan Dolinsky, 2021. "A Note on Utility Maximization with Proportional Transaction Costs and Stability of Optimal Portfolios," Papers 2107.01568, arXiv.org, revised Sep 2021.
    5. 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.
    6. Friedrich Hubalek & Walter Schachermayer, 2021. "Convergence of optimal expected utility for a sequence of binomial models," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1315-1331, October.

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    More about this item

    Keywords

    Utility maximisation; Proportional transaction costs; Extended weak convergence; Meyer–Zheng topology;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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