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Discrete-time behavioral portfolio selection under cumulative prospect theory

Author

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  • Shi, Yun
  • Cui, Xiangyu
  • Li, Duan

Abstract

We formulate and study three multi-period behavioral portfolio selection models under cumulative prospect theory: (i) S-shaped utility maximization without probability weighting in a market with one risky asset; (ii) S-shaped utility maximization without probability weighting in a market with multiple risky assets which follow a joint elliptical distribution; and (iii) S-shaped utility maximization with inverse-S-shaped probability weighting in a market with one risky asset. For the first two time consistent models, we identify the well-posedness conditions and derive the semi-analytical optimal policies. For the third time inconsistent model, we assume that the investor is aware of the time inconsistency but is unable to commit to his initial plan of action. Then, we reformulate the model into an intrapersonal game model and derive the semi-analytical subgame perfect Nash equilibrium (time consistent) policy under well-posedness condition. All the three policies take a piecewise linear feedback form. Our analysis of the three models not only partially explains the well documented phenomena of non-participation puzzle and horizon effect, but also extends the two fund separation theorem into multi-period S-shaped utility setting and pushes forward the study on time inconsistency issue incurred by probability weighting.

Suggested Citation

  • Shi, Yun & Cui, Xiangyu & Li, Duan, 2015. "Discrete-time behavioral portfolio selection under cumulative prospect theory," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 283-302.
  • Handle: RePEc:eee:dyncon:v:61:y:2015:i:c:p:283-302
    DOI: 10.1016/j.jedc.2015.10.002
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    References listed on IDEAS

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    Cited by:

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    3. Fortin, Ines & Hlouskova, Jaroslava, 2024. "Prospect theory and asset allocation," The Quarterly Review of Economics and Finance, Elsevier, vol. 94(C), pages 214-240.
    4. Xiangyu Cui & Yun Shi & Lu Xu, 2017. "Alleviating time inconsistent behaviors via a competition scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 357-372, August.
    5. Baule, Rainer & Korn, Olaf & Kuntz, Laura-Chloé, 2019. "Markowitz with regret," Journal of Economic Dynamics and Control, Elsevier, vol. 103(C), pages 1-24.
    6. Zhang, Cheng & Gong, Xiaomin & Zhang, Jingshu & Chen, Zhiwei, 2023. "Dynamic portfolio allocation for financial markets: A perspective of competitive-cum-compensatory strategy," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 84(C).
    7. Lou, Youcheng & Strub, Moris S. & Li, Duan & Wang, Shouyang, 2021. "The impact of a reference point determined by social comparison on wealth growth and inequality," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    8. Cui, Xiangyu & Li, Duan & Shi, Yun, 2017. "Self-coordination in time inconsistent stochastic decision problems: A planner–doer game framework," Journal of Economic Dynamics and Control, Elsevier, vol. 75(C), pages 91-113.

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    More about this item

    Keywords

    Multi-period portfolio selection; S-shaped utility; Probability weighting; Time consistent policy; Two-fund separation; Non-participation puzzle and horizon effect;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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