IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v110y2023icp82-105.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668723000203
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2023.02.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
    2. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    3. Xue Dong He & Xun Yu Zhou, 2016. "Hope, Fear, And Aspirations," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 3-50, January.
    4. Zuo Quan Xu, 2013. "A New Characterization of Comonotonicity and its Application in Behavioral Finance," Papers 1311.6080, arXiv.org, revised Jun 2014.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    7. 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.
    8. 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.
    9. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    12. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    13. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    14. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    15. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Jianzhou & Lv, Mengzheng & Wang, Shuai & Gao, Jialu & Zhao, Yang & Wang, Qiangqiang, 2024. "Can multi-period auto-portfolio systems improve returns? Evidence from Chinese and U.S. stock markets," International Review of Financial Analysis, Elsevier, vol. 95(PB).
    2. Calvin Mudzingiri, 2024. "The Effect of Financial Literacy Confidence on Financial Risk Preference Confidence. A Lab Experiment Approach," SAGE Open, , vol. 14(2), pages 21582440241, May.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    2. Marcos Escobar-Anel & Michel Kschonnek & Rudi Zagst, 2022. "Portfolio optimization: not necessarily concave utility and constraints on wealth and allocation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 101-140, February.
    3. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, February.
    4. van Bilsen, Servaas & Laeven, Roger J.A., 2020. "Dynamic consumption and portfolio choice under prospect theory," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 224-237.
    5. Xue Dong He & Zhaoli Jiang & Steven Kou, 2020. "Portfolio Selection under Median and Quantile Maximization," Papers 2008.10257, arXiv.org, revised Mar 2021.
    6. Bi, Xiuchun & Cui, Zhenyu & Fan, Jiacheng & Yuan, Lvning & Zhang, Shuguang, 2023. "Optimal investment problem under behavioral setting: A Lagrange duality perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 156(C).
    7. Zuo Quan Xu, 2018. "Pareto optimal moral-hazard-free insurance contracts in behavioral finance framework," Papers 1803.02546, arXiv.org, revised Aug 2021.
    8. Servaas van Bilsen & Roger J. A. Laeven & Theo E. Nijman, 2020. "Consumption and Portfolio Choice Under Loss Aversion and Endogenous Updating of the Reference Level," Management Science, INFORMS, vol. 66(9), pages 3927-3955, September.
    9. Zuo Quan Xu, 2021. "Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory," Papers 2108.06940, arXiv.org, revised Aug 2022.
    10. Zuo Quan Xu, 2014. "A Note on the Quantile Formulation," Papers 1403.7269, arXiv.org, revised Apr 2014.
    11. Curatola, Giuliano, 2017. "Optimal portfolio choice with loss aversion over consumption," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 345-358.
    12. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2019. "Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion," Papers 1904.01745, arXiv.org.
    13. Rania HENTATI & Jean-Luc PRIGENT, 2010. "Structured Portfolio Analysis under SharpeOmega Ratio," EcoMod2010 259600073, EcoMod.
    14. Stephen G Dimmock & Roy Kouwenberg & Olivia S Mitchell & Kim Peijnenburg, 2021. "Household Portfolio Underdiversification and Probability Weighting: Evidence from the Field," The Review of Financial Studies, Society for Financial Studies, vol. 34(9), pages 4524-4563.
    15. 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.
    16. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2021. "Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion," Mathematical Finance, Wiley Blackwell, vol. 31(2), pages 683-721, April.
    17. Curatola, Giuliano, 2016. "Optimal consumption and portfolio choice with loss aversion," SAFE Working Paper Series 130, Leibniz Institute for Financial Research SAFE.
    18. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    19. Li, Yan & Mi, Hui, 2021. "Portfolio optimization under safety first expected utility with nonlinear probability distortion," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    20. Luciano de Castro & Antonio F. Galvao & Gabriel Montes-Rojas & Jose Olmo, 2022. "Portfolio selection in quantile decision models," Annals of Finance, Springer, vol. 18(2), pages 133-181, June.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:110:y:2023:i:c:p:82-105. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.