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Dynamic Mean–Variance Portfolio Optimization with Value-at-Risk Constraint in Continuous Time

Author

Listed:
  • Tongyao Wang

    (Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China)

  • Qitong Pan

    (School of Economics and Management, Fuzhou University, Fuzhou 350108, China)

  • Weiping Wu

    (School of Economics and Management, Fuzhou University, Fuzhou 350108, China)

  • Jianjun Gao

    (School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, China)

  • Ke Zhou

    (Business School, Hunan University, Changsha 410082, China)

Abstract

Recognizing the importance of incorporating different risk measures in the portfolio management model, this paper examines the dynamic mean-risk portfolio optimization problem using both variance and value at risk (VaR) as risk measures. By employing the martingale approach and integrating the quantile optimization technique, we provide a solution framework for this problem. We demonstrate that, under a general market setting, the optimal terminal wealth may exhibit different patterns. When the market parameters are deterministic, we derive the closed-form solution for this problem. Examples are provided to illustrate the solution procedure of our method and demonstrate the benefits of our dynamic portfolio model compared to its static counterpart.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2268-:d:1439159
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    References listed on IDEAS

    as
    1. Diana Roman & Kenneth Darby-Dowman & Gautam Mitra, 2007. "Mean-risk models using two risk measures: a multi-objective approach," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 443-458.
    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. Ahmadi-Javid, Amir & Fallah-Tafti, Malihe, 2019. "Portfolio optimization with entropic value-at-risk," European Journal of Operational Research, Elsevier, vol. 279(1), pages 225-241.
    4. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    5. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    6. Pengyu Wei, 2018. "Risk management with weighted VaR," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1020-1060, October.
    7. Hanqing Jin & Xun Yu Zhou, 2008. "Behavioral Portfolio Selection In Continuous Time," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 385-426, July.
    8. 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.
    9. 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.
    10. Xiangyu Cui & Duan Li & Xun Li, 2017. "Mean-Variance Policy For Discrete-Time Cone-Constrained Markets: Time Consistency In Efficiency And The Minimum-Variance Signed Supermartingale Measure," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 471-504, April.
    11. Xue Dong He & Xun Yu Zhou, 2011. "Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment," Management Science, INFORMS, vol. 57(2), pages 315-331, February.
    12. Benati, Stefano & Rizzi, Romeo, 2007. "A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 423-434, January.
    13. 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.
    14. Francesco Cesarone & Manuel L. Martino & Fabio Tardella, 2023. "Mean-Variance-VaR portfolios: MIQP formulation and performance analysis," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 1043-1069, September.
    15. 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.
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