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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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