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Optimal investment with transaction costs under cumulative prospect theory in discrete time

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Abstract

We study optimal investment problems under the framework of cumulative prospect theory (CPT). A CPT investor makes investment decisions in a single-period financial market with transaction costs. The objective is to seek the optimal investment strategy that maximizes the prospect value of the investor’s final wealth. We obtain the optimal investment strategy explicitly in two examples. An economic analysis is conducted to investigate the impact of the transaction costs and risk aversion on the optimal investment strategy.

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Notes

  1. Daniel Kahneman was awarded the 2002 Nobel Memorial Prize in Economic Sciences for his pioneering work on the psychology of decision-making and behavioral economics (notably, prospect theory and cumulative prospect theory).

  2. In this case, the replication strategy involves long the risky asset. \(\theta _\xi \) and \(x_\xi \) are solved from \( (1+r) \cdot (x_\xi - \theta _\xi ) + (1-\lambda )u \cdot \theta _\xi = \xi _u \text { and } (1+r) \cdot (x_\xi - \theta _\xi ) + (1-\lambda )d \cdot \theta _\xi = \xi _d. \)

  3. In this case, the replication strategy involves short the risky asset. \(\theta _\xi \) and \(x_\xi \) are solved from \( (1+r) \cdot (x_\xi - (1-\lambda )\theta _\xi ) + u \cdot \theta _\xi = \xi _u \text { and } (1+r) \cdot (x_\xi - (1-\lambda )\theta _\xi ) + d \cdot \theta _\xi = \xi _d. \)

  4. The results explain the superscript notations in \(\varXi ^b\) and \(\varXi ^s\) (“b” stands for “buy” and “s” stands for “sell”).

  5. Data source: Thomson Reuters Eikon. Access from the Chair of Mathematical Finance at the Technical University of Munich is greatly appreciated.

  6. Data source: Yahoo Finance https://uk.finance.yahoo.com/q/hp?s=%5EFTSE.

  7. The increasing property of \(\theta _1\) with respect to \(\beta \) is not that noticeable in Fig. 4, but is clearly supported by numerical values.

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Acknowledgements

The first author BZ acknowledges the financial support from the Technical University of Munich (TUM) through the TUM foundation fellowship. This work was done when BZ was a postdoctoral fellow at the Chair of Mathematical Finance of TUM. We are thankful to two anonymous referees for valuable comments and suggestions.

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  1. Department of Applied Mathematics, University of Washington, Seattle, WA, USA

    Bin Zou

  2. Chair of Mathematical Finance, Technical University of Munich, Parkring 11, Garching-Hochbrück, 85748, Munich, Germany

    Rudi Zagst

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  1. Bin Zou
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  2. Rudi Zagst
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Correspondence to Rudi Zagst.

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Zou, B., Zagst, R. Optimal investment with transaction costs under cumulative prospect theory in discrete time. Math Finan Econ 11, 393–421 (2017). https://doi.org/10.1007/s11579-017-0186-z

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