IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v203y2024i1d10.1007_s10957-024-02537-9.html
   My bibliography  Save this article

Precommitted Strategies with Initial-Time and Intermediate-Time Value-at-Risk Constraints

Author

Listed:
  • Chufang Wu

    (Shenzhen Polytechnic University)

  • Jia-Wen Gu

    (Southern University of Science and Technology)

  • Wai-Ki Ching

    (The University of Hong Kong)

  • Chi-Wing Wong

    (The University of Hong Kong)

Abstract

This paper considers the expected utility portfolio optimization problem with initial-time and intermediate-time Value-at-Risk constraints on terminal wealth. We derive the closed-form solutions which are optimal among all feasible controls at initial time, i.e., precommitted strategies. Moreover, the precommitted strategies are also optimal at the intermediate time for “bad” market states. A contingent claim on Merton’s portfolio is constructed to replicate the optimal portfolio. We find that risk management with intermediate-time risk constraints is prudent in hedging “bad” intermediate market states and performs significantly better than the one terminal-wealth risk constraint solutions under the relative loss ratio measure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02537-9
    DOI: 10.1007/s10957-024-02537-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-024-02537-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-024-02537-9?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. 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.
    2. Bräutigam, Marcel & Kratz, Marie, 2023. "How do empirical estimators of popular risk measures impact pro-cyclicality?," Annals of Actuarial Science, Cambridge University Press, vol. 17(3), pages 547-579, November.
    3. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    4. Gundel, Anne & Weber, Stefan, 2007. "Robust utility maximization with limited downside risk in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1663-1688, November.
    5. Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 997-1015, April.
    6. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    7. Gundel, Anne & Weber, Stefan, 2008. "Utility maximization under a shortfall risk constraint," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1126-1151, December.
    8. 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.
    9. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    10. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    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. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    13. Henry R. Richardson, 1989. "A Minimum Variance Result in Continuous Trading Portfolio Optimization," Management Science, INFORMS, vol. 35(9), pages 1045-1055, September.
    14. Peter Lakner & Lan Ma Nygren, 2006. "Portfolio Optimization With Downside Constraints," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 283-299, April.
    15. Jang, Bong-Gyu & Park, Seyoung, 2016. "Ambiguity and optimal portfolio choice with Value-at-Risk constraint," Finance Research Letters, Elsevier, vol. 18(C), pages 158-176.
    16. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    17. Cuoco, Domenico & Liu, Hong, 2006. "An analysis of VaR-based capital requirements," Journal of Financial Intermediation, Elsevier, vol. 15(3), pages 362-394, 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. 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.
    2. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    3. Jang, Bong-Gyu & Park, Seyoung, 2016. "Ambiguity and optimal portfolio choice with Value-at-Risk constraint," Finance Research Letters, Elsevier, vol. 18(C), pages 158-176.
    4. Thai Nguyen & Mitja Stadje, 2018. "Optimal investment for participating insurance contracts under VaR-Regulation," Papers 1805.09068, arXiv.org, revised Jul 2019.
    5. John Armstrong & Damiano Brigo & Alex S. L. Tse, 2024. "The importance of dynamic risk constraints for limited liability operators," Annals of Operations Research, Springer, vol. 336(1), pages 861-898, May.
    6. Fangyuan Zhang, 2023. "Non-concave portfolio optimization with average value-at-risk," Mathematics and Financial Economics, Springer, volume 17, number 3, February.
    7. 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.
    8. Traian A. Pirvu & Gordan Žitković, 2009. "Maximizing The Growth Rate Under Risk Constraints," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 423-455, July.
    9. 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.
    10. Frank Seifried, 2010. "Optimal investment with deferred capital gains taxes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 181-199, February.
    11. Kraft, Holger & Steffensen, Mogens, 2012. "A dynamic programming approach to constrained portfolios," CFS Working Paper Series 2012/07, Center for Financial Studies (CFS).
    12. Das, Sanjiv R. & Statman, Meir, 2013. "Options and structured products in behavioral portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 137-153.
    13. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    14. Marcos Escobar-Anel & Yevhen Havrylenko & Rudi Zagst, 2022. "Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model," Papers 2208.14152, arXiv.org, revised Jul 2024.
    15. Dong, Yinghui & Zheng, Harry, 2020. "Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan," European Journal of Operational Research, Elsevier, vol. 281(2), pages 341-356.
    16. 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.
    17. Dong, Yinghui & Zheng, Harry, 2019. "Optimal investment of DC pension plan under short-selling constraints and portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 47-59.
    18. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    19. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
    20. Marcos Escobar-Anel, 2022. "A dynamic programming approach to path-dependent constrained portfolios," Annals of Operations Research, Springer, vol. 315(1), pages 141-157, August.

    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:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02537-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.