IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v322y2025i1p325-340.html
   My bibliography  Save this article

Dynamic growth-optimal portfolio choice under risk control

Author

Listed:
  • Wei, Pengyu
  • Xu, Zuo Quan

Abstract

This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. It is a growth-optimal portfolio choice problem under risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which is a generalization of Value-at-Risk (VaR) and Expected Shortfall (ES). We characterize the optimal terminal wealth and obtain analytical expressions when risk is measured by VaR or ES. We demonstrate that using VaR increases losses while ES reduces losses during market downturns. Moreover, the efficient frontier is a concave curve that connects the minimum-risk portfolio with the growth optimal portfolio, as opposed to the vertical line when WVaR is used on terminal wealth, and thus allows for a meaningful characterization of the risk-return trade-off and aids investors in setting reasonable investment targets. We also apply our model to benchmarking and illustrate how investors with benchmarking may overperform/underperform the market depending on economic conditions.

Suggested Citation

  • Wei, Pengyu & Xu, Zuo Quan, 2025. "Dynamic growth-optimal portfolio choice under risk control," European Journal of Operational Research, Elsevier, vol. 322(1), pages 325-340.
    • Handle: RePEc:eee:ejores:v:322:y:2025:i:1:p:325-340
    DOI: 10.1016/j.ejor.2024.10.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724008464
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.10.043?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. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    3. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
    4. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    5. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    6. Xue Dong He & Hanqing Jin & Xun Yu Zhou, 2015. "Dynamic Portfolio Choice When Risk Is Measured by Weighted VaR," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 773-796, March.
    7. Zuo Quan Xu, 2013. "A New Characterization of Comonotonicity and its Application in Behavioral Finance," Papers 1311.6080, arXiv.org, revised Jun 2014.
    8. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    9. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    10. 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.
    11. repec:dau:papers:123456789/5392 is not listed on IDEAS
    12. Edward O. Thorp, 2011. "The Kelly Criterion in Blackjack Sports Betting, and the Stock Market," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 54, pages 789-832, World Scientific Publishing Co. Pte. Ltd..
    13. Lioui, Abraham, 2013. "Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1066-1096.
    14. Jia-Wen Gu & Mogens Steffensen & Harry Zheng, 2021. "A note on - vs. -expected loss portfolio constraints," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 263-270, February.
    15. repec:dau:papers:123456789/2317 is not listed on IDEAS
    16. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Does the Basle Capital Accord reduce bank fragility? An assessment of the value-at-risk approach," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1631-1660, October.
    17. Xue Dong He & Zhaoli Jiang, 2022. "Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 587-615, February.
    18. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    19. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    20. Bi, Junna & Jin, Hanqing & Meng, Qingbin, 2018. "Behavioral mean-variance portfolio selection," European Journal of Operational Research, Elsevier, vol. 271(2), pages 644-663.
    21. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
    22. Suleyman Basak & Alex Shapiro & Lucie Teplá, 2006. "Risk Management with Benchmarking," Management Science, INFORMS, vol. 52(4), pages 542-557, April.
    23. Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
    24. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    25. Pengyu Wei, 2018. "Risk management with weighted VaR," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1020-1060, October.
    26. Erik Aurell & Roberto Baviera & Ola Hammarlid & Maurizio Serva & Angelo Vulpiani, 2000. "A General Methodology To Price And Hedge Derivatives In Incomplete Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-24.
    27. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    28. Gao, Jianjun & Xiong, Yan & Li, Duan, 2016. "Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time," European Journal of Operational Research, Elsevier, vol. 249(2), pages 647-656.
    29. Bernard, Carole & Cui, Xuecan, 2023. "Impact of systemic risk regulation on optimal policies and asset prices," Journal of Banking & Finance, Elsevier, vol. 154(C).
    30. Alexandre Adam & Mohamed Houkari & Jean-Paul Laurent, 2008. "Spectral risk measures and portfolio selection," Post-Print hal-03676385, HAL.
    31. Hanqing Jin & Harry Markowitz & Xun Yu Zhou, 2006. "A Note On Semivariance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 53-61, January.
    32. Carole Bernard & Phelim P. Boyle & Steven Vanduffel, 2014. "Explicit Representation of Cost-Efficient Strategies," Finance, Presses universitaires de Grenoble, vol. 35(2), pages 5-55.
    33. Tomasz R. Bielecki & Hanqing Jin & Stanley R. Pliska & Xun Yu Zhou, 2005. "Continuous‐Time Mean‐Variance Portfolio Selection With Bankruptcy Prohibition," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 213-244, April.
    34. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, April.
    35. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    Full references (including those not matched with items on IDEAS)

    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. Pengyu Wei & Zuo Quan Xu, 2021. "Dynamic growth-optimum portfolio choice under risk control," Papers 2112.14451, arXiv.org.
    2. Xue Dong He & Hanqing Jin & Xun Yu Zhou, 2015. "Dynamic Portfolio Choice When Risk Is Measured by Weighted VaR," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 773-796, March.
    3. Weiping Wu & Yu Lin & Jianjun Gao & Ke Zhou, 2023. "Mean-variance hybrid portfolio optimization with quantile-based risk measure," Papers 2303.15830, arXiv.org, revised Apr 2023.
    4. Fießinger, Felix & Stadje, Mitja, 2025. "Time-consistent asset allocation for risk measures in a Lévy market," European Journal of Operational Research, Elsevier, vol. 321(2), pages 676-695.
    5. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Oct 2024.
    6. Jianming Xia, 2023. "Benchmark Beating with the Increasing Convex Order," Papers 2311.01692, arXiv.org.
    7. Jianming Xia, 2021. "Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures," Papers 2112.02284, arXiv.org.
    8. Mario Brandtner, 2016. "Spektrale Risikomaße: Konzeption, betriebswirtschaftliche Anwendungen und Fallstricke," Management Review Quarterly, Springer, vol. 66(2), pages 75-115, April.
    9. Brandtner, Mario, 2013. "Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5526-5537.
    10. Ke Zhou & Jiangjun Gao & Duan Li & Xiangyu Cui, 2017. "Dynamic mean–VaR portfolio selection in continuous time," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1631-1643, October.
    11. Tongyao Wang & Qitong Pan & Weiping Wu & Jianjun Gao & Ke Zhou, 2024. "Dynamic Mean–Variance Portfolio Optimization with Value-at-Risk Constraint in Continuous Time," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    12. Taras Bodnar & Mathias Lindholm & Erik Thorsén & Joanna Tyrcha, 2021. "Quantile-based optimal portfolio selection," Computational Management Science, Springer, vol. 18(3), pages 299-324, July.
    13. Alexander, Gordon J. & Baptista, Alexandre M., 2009. "Stress testing by financial intermediaries: Implications for portfolio selection and asset pricing," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 65-92, January.
    14. Gao, Jianjun & Xiong, Yan & Li, Duan, 2016. "Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time," European Journal of Operational Research, Elsevier, vol. 249(2), pages 647-656.
    15. Xue Dong He & Zhaoli Jiang, 2020. "Optimal Payoff under the Generalized Dual Theory of Choice," Papers 2012.00345, arXiv.org.
    16. De Gennaro Aquino, Luca & Sornette, Didier & Strub, Moris S., 2023. "Portfolio selection with exploration of new investment assets," European Journal of Operational Research, Elsevier, vol. 310(2), pages 773-792.
    17. Guan, Guohui & Liang, Zongxia, 2016. "Optimal management of DC pension plan under loss aversion and Value-at-Risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 224-237.
    18. Omid Momen & Akbar Esfahanipour & Abbas Seifi, 2020. "A robust behavioral portfolio selection: model with investor attitudes and biases," Operational Research, Springer, vol. 20(1), pages 427-446, March.
    19. 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.
    20. Brandtner, Mario & Kürsten, Wolfgang & Rischau, Robert, 2018. "Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity," European Journal of Operational Research, Elsevier, vol. 264(2), pages 707-716.

    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:ejores:v:322:y:2025:i:1:p:325-340. 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/eor .

    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.