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Optimal investment for retail investors

Author

Listed:
  • Christoph Belak
  • Lukas Mich
  • Frank T. Seifried

Abstract

We study optimal portfolio decisions for a retail investor that faces a strictly positive transaction cost in a classical Black‐Scholes market. We provide a construction of optimal trading strategies and characterize the value function as the unique viscosity solution of the associated quasi‐variational inequalities. Moreover, we numerically investigate the optimal trading regions for a variety of real‐world cost structures faced by retail investors. We find that the cost structure has a strong effect on the qualitative shape of the no‐trading region and optimal strategies.

Suggested Citation

  • Christoph Belak & Lukas Mich & Frank T. Seifried, 2022. "Optimal investment for retail investors," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 555-594, April.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:2:p:555-594
    DOI: 10.1111/mafi.12336
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    References listed on IDEAS

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    8. 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.
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    Cited by:

    1. Carole Bernard & Gero Junike & Thibaut Lux & Steven Vanduffel, 2024. "Cost-efficient payoffs under model ambiguity," Finance and Stochastics, Springer, vol. 28(4), pages 965-997, October.
    2. Erhan Bayraktar & Bingyan Han, 2025. "Goal-based portfolio selection with mental accounting," Papers 2506.06654, arXiv.org, revised Jun 2025.
    3. Florian Krach & Josef Teichmann & Hanna Wutte, 2024. "Robust Utility Optimization via a GAN Approach," Papers 2403.15243, arXiv.org, revised Sep 2025.
    4. Erhan Bayraktar & Bingyan Han & Jingjie Zhang, 2025. "Goal-based portfolio selection with fixed transaction costs," Papers 2510.21650, arXiv.org.
    5. Christoph Knochenhauer & Alexander Merkel & Yufei Zhang, 2024. "Optimal Investment with Costly Expert Opinions," Papers 2409.11569, arXiv.org.
    6. Chen, An & Vanduffel, Steven & Wilke, Morten, 2025. "Optimal payoffs under smooth ambiguity," European Journal of Operational Research, Elsevier, vol. 320(3), pages 754-764.

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