IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v186y2020i3d10.1007_s10957-020-01724-8.html
   My bibliography  Save this article

A Level-Set Approach for Stochastic Optimal Control Problems Under Controlled-Loss Constraints

Author

Listed:
  • Géraldine Bouveret

    (Nanyang Technological University)

  • Athena Picarelli

    (Università di Verona)

Abstract

We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton–Jacobi–Bellman equation usually calls for strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in the absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then solve the latter by a level-set approach. With this approach, state constraints are managed through an exact penalization technique.

Suggested Citation

  • Géraldine Bouveret & Athena Picarelli, 2020. "A Level-Set Approach for Stochastic Optimal Control Problems Under Controlled-Loss Constraints," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 779-805, September.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:3:d:10.1007_s10957-020-01724-8
    DOI: 10.1007/s10957-020-01724-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01724-8
    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/s10957-020-01724-8?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. H. Fink & S. Geissel & J. Herbinger & F. T. Seifried, 2019. "Portfolio Optimization with Optimal Expected Utility Risk Measures," Working Paper Series 2019-07, University of Trier, Research Group Quantitative Finance and Risk Analysis.
    2. 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.
    3. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    4. Cyril B'en'ezet & Jean-Franc{c}ois Chassagneux & Christoph Reisinger, 2019. "A numerical scheme for the quantile hedging problem," Papers 1902.11228, arXiv.org.
    5. Géraldine Bouveret, 2019. "Dual Representation of the Cost of Designing a Portfolio Satisfying Multiple Risk Constraints," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(3), pages 222-256, May.
    6. Bruno Bouchard & Jean-François Chassagneux & Géraldine Bouveret, 2016. "A backward dual representation for the quantile hedging of Bermudan options," Post-Print hal-01069270, HAL.
    7. Géraldine Bouveret, 2018. "Portfolio Optimization Under A Quantile Hedging Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-36, November.
    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. Géraldine Bouveret, 2018. "Portfolio Optimization Under A Quantile Hedging Constraint," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-36, November.
    2. Areski Cousin & Ying Jiao & Christian y Robert & Olivier David Zerbib, 2021. "Optimal asset allocation subject to withdrawal risk and solvency constraints," Working Papers hal-03244380, HAL.
    3. Ying Jiao & Olivier Klopfenstein & Peter Tankov, 2013. "Hedging under multiple risk constraints," Papers 1309.5094, arXiv.org.
    4. De Franco, Carmine & Tankov, Peter, 2011. "Portfolio insurance under a risk-measure constraint," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 361-370.
    5. 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.
    6. Cousin, Areski & Jiao, Ying & Robert, Christian Y. & Zerbib, Olivier David, 2016. "Asset allocation strategies in the presence of liability constraints," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 327-338.
    7. Ying Jiao & Olivier Klopfenstein & Peter Tankov, 2017. "Hedging under multiple risk constraints," Finance and Stochastics, Springer, vol. 21(2), pages 361-396, April.
    8. Palomba, Giulio & Riccetti, Luca, 2012. "Portfolio frontiers with restrictions to tracking error volatility and value at risk," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2604-2615.
    9. Roxana Dumitrescu & Romuald Elie & Wissal Sabbagh & Chao Zhou, 2017. "A new Mertens decomposition of $\mathscr{Y}^{g,\xi}$-submartingale systems. Application to BSDEs with weak constraints at stopping times," Papers 1708.05957, arXiv.org, revised May 2023.
    10. Dumitrescu, Roxana & Elie, Romuald & Sabbagh, Wissal & Zhou, Chao, 2023. "A new Mertens decomposition of Yg,ξ-submartingale systems. Application to BSDEs with weak constraints at stopping times," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 183-205.
    11. Bayraktar, Erhan & Young, Virginia R., 2008. "Maximizing utility of consumption subject to a constraint on the probability of lifetime ruin," Finance Research Letters, Elsevier, vol. 5(4), pages 204-212, December.
    12. Cyril B'en'ezet & Jean-Franc{c}ois Chassagneux & Mohan Yang, 2023. "An optimal transport approach for the multiple quantile hedging problem," Papers 2308.01121, arXiv.org.
    13. 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.
    14. 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.
    15. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    16. Escobar-Anel, Marcos & Havrylenko, Yevhen & Kschonnek, Michel & Zagst, Rudi, 2022. "Decrease of capital guarantees in life insurance products: Can reinsurance stop it?," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 14-40.
    17. Mei Choi Chiu & Hoi Ying Wong & Duan Li, 2012. "Roy’s Safety‐First Portfolio Principle in Financial Risk Management of Disastrous Events," Risk Analysis, John Wiley & Sons, vol. 32(11), pages 1856-1872, November.
    18. Oliver Janke & Qinghua Li, 2015. "Portfolio Optimization under Shortfall Risk Constraint," Papers 1501.07480, arXiv.org, revised Apr 2016.
    19. Gundel, Anne & Weber, Stefan, 2008. "Utility maximization under a shortfall risk constraint," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1126-1151, December.
    20. Christelle Dleuna Nyoumbi & Antoine Tambue, 2023. "A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 1-34, January.

    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:186:y:2020:i:3:d:10.1007_s10957-020-01724-8. 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.