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Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis

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  • Gary Quek
  • Colin Atkinson

Abstract

In this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length.

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  • Gary Quek & Colin Atkinson, 2017. "Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(2), pages 77-111, March.
    • Handle: RePEc:taf:apmtfi:v:24:y:2017:i:2:p:77-111
    DOI: 10.1080/1350486X.2017.1342551
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    Cited by:

    1. Escobar-Anel, Marcos & Gollart, Maximilian & Zagst, Rudi, 2022. "Closed-form portfolio optimization under GARCH models," Operations Research Perspectives, Elsevier, vol. 9(C).
    2. Yingting Miao & Qiang Zhang, 2023. "Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility," Papers 2304.07672, arXiv.org.
    3. Xi Zhang & Xu Wu & Linlin Zhang & Zhonglu Chen, 2022. "The Evaluation of Mean-Detrended Cross-Correlation Analysis Portfolio Strategy for Multiple risk Assets," Evaluation Review, , vol. 46(2), pages 138-164, April.

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