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Risk management with weighted VaR

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  • Pengyu Wei

Abstract

This article studies the optimal portfolio selection of expected utility‐maximizing investors who must also manage their market‐risk exposures. The risk is measured by a so‐called weighted value‐at‐risk (WVaR) risk measure, which is a generalization of both value‐at‐risk (VaR) and expected shortfall (ES). The feasibility, well‐posedness, and existence of the optimal solution are examined. We obtain the optimal solution (when it exists) and show how risk measures change asset allocation patterns. In particular, we characterize three classes of risk measures: the first class will lead to models that do not admit an optimal solution, the second class can give rise to endogenous portfolio insurance, and the third class, which includes VaR and ES, two popular regulatory risk measures, will allow economic agents to engage in “regulatory capital arbitrage,” incurring larger losses when losses occur.

Suggested Citation

  • Pengyu Wei, 2018. "Risk management with weighted VaR," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1020-1060, October.
    • Handle: RePEc:bla:mathfi:v:28:y:2018:i:4:p:1020-1060
    DOI: 10.1111/mafi.12160
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    Citations

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    Cited by:

    1. 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.
    2. Jing Peng & Pengyu Wei & Zuo Quan Xu, 2022. "Relative growth rate optimization under behavioral criterion," Papers 2211.05402, arXiv.org.
    3. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    4. Huang, Zhenzhen & Wei, Pengyu & Weng, Chengguo, 2024. "Tail mean-variance portfolio selection with estimation risk," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 218-234.
    5. 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.
    6. Jianming Xia, 2021. "Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures," Papers 2112.02284, arXiv.org.
    7. Jianming Xia, 2023. "Benchmark Beating with the Increasing Convex Order," Papers 2311.01692, arXiv.org.
    8. Bernard, Carole & Cui, Xuecan, 2023. "Impact of systemic risk regulation on optimal policies and asset prices," Journal of Banking & Finance, Elsevier, vol. 154(C).
    9. An Chen & Mitja Stadje & Fangyuan Zhang, 2020. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Papers 2002.02229, arXiv.org, revised Jun 2022.
    10. Pengyu Wei & Zuo Quan Xu, 2021. "Dynamic growth-optimum portfolio choice under risk control," Papers 2112.14451, arXiv.org.
    11. 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.
    12. 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).
    13. Zongxia Liang & Yang Liu & Litian Zhang, 2021. "A Framework of State-dependent Utility Optimization with General Benchmarks," Papers 2101.06675, arXiv.org, revised Dec 2023.

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