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

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  • 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
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    References listed on IDEAS

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    1. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    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. 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.
    4. 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.
    5. 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.
    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. 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.
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