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Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory

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  • Mi, Hui
  • Xu, Zuo Quan

Abstract

This paper investigates two optimal portfolio selection problems for a rank-dependent utility investor who needs to manage his risk exposure: one with a single Value-at-Risk (VaR) constraint and the other with joint VaR and portfolio insurance constraints. The two models generalize existing models under expected utility theory and behavioral theory. The martingale method, quantile formulation, and relaxation method are used to obtain explicit optimal solutions. We have specifically identified an equivalent condition under which the VaR constraint is effective. A numerical analysis is carried out to demonstrate theoretical results, and additional financial insights are presented. We find that, in bad market states, the risk of the optimal investment outcome is reduced when compared to existing models without or with one constraint.

Suggested Citation

  • Mi, Hui & Xu, Zuo Quan, 2023. "Optimal portfolio selection with VaR and portfolio insurance constraints under rank-dependent expected utility theory," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 82-105.
    • Handle: RePEc:eee:insuma:v:110:y:2023:i:c:p:82-105
    DOI: 10.1016/j.insmatheco.2023.02.004
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    References listed on IDEAS

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    1. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
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    7. Xue Dong He & Xun Yu Zhou, 2016. "Hope, Fear, And Aspirations," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 3-50, January.
    8. Zuo Quan Xu, 2013. "A New Characterization of Comonotonicity and its Application in Behavioral Finance," Papers 1311.6080, arXiv.org, revised Jun 2014.
    9. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
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    12. Chen, An & Nguyen, Thai & Stadje, Mitja, 2018. "Optimal investment under VaR-Regulation and Minimum Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 194-209.
    13. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
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    Cited by:

    1. Hui Mi & Zuo Quan Xu & Dongfang Yang, 2023. "Optimal Management of DC Pension Plan with Inflation Risk and Tail VaR Constraint," Papers 2309.01936, arXiv.org.

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    More about this item

    Keywords

    Portfolio optimization; Rank-dependent expected utility; Quantile formulation; Relaxation method; VaR constraint;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G41 - Financial Economics - - Behavioral Finance - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making in Financial Markets
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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