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Risk management with multiple VaR constraints

Author

Listed:
  • An Chen

    (Universität Ulm)

  • Thai Nguyen

    (Universität Ulm
    University of Economics HCM City)

  • Mitja Stadje

    (Universität Ulm)

Abstract

We study a utility maximization problem under multiple Value-at-Risk (VaR)-type constraints. The optimization framework is particularly important for financial institutions which have to follow short-time VaR-type regulations under some realistic regulatory frameworks like Solvency II, but need to serve long-term liabilities. Deriving closed-form solutions, we show that risk management using multiple VaR constraints is more useful for loss prevention at intertemporal time instances compared with the well-known result of the one-VaR problem in Basak and Shapiro (Rev Financ Stud 14:371–405, 2001), confirming the numerical analysis of Shi and Werker (J Bank Finance 36(12):3227–3238, 2012). In addition, the multiple-VaR solution at maturity on average dominates the one-VaR solution in a wide range of intermediate market scenarios, but performs worse in good and very bad market scenarios. The range of these very bad market scenarios is however rather limited. Finally, we show that it is preferable to reach a fixed terminal state through insured intertemporal states rather than through extreme up and down movements, showing that a multiple-VaR framework induces a preference for less volatility.

Suggested Citation

  • An Chen & Thai Nguyen & Mitja Stadje, 2018. "Risk management with multiple VaR constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 297-337, October.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:2:d:10.1007_s00186-018-0637-1
    DOI: 10.1007/s00186-018-0637-1
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    References listed on IDEAS

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    Cited by:

    1. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    2. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    3. Chufang Wu & Jia-Wen Gu & Wai-Ki Ching & Chi-Wing Wong, 2024. "Precommitted Strategies with Initial-Time and Intermediate-Time Value-at-Risk Constraints," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 880-919, October.
    4. Chen, An & Stadje, Mitja & Zhang, Fangyuan, 2024. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 114-129.

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    More about this item

    Keywords

    Value at Risk; Optimal portfolio; Multiple risk constraints; Risk management; Solvency II regulation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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