A level-set approach for stochastic optimal control problems under controlled-loss constraints
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 additional strong assumptions on the dynamics of the proces...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/143416 |
| _version_ | 1811695040027688960 |
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| author | Bouveret, Geraldine Picarelli, Athena |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Bouveret, Geraldine Picarelli, Athena |
| author_sort | Bouveret, Geraldine |
| collection | NTU |
| description | 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 additional strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then apply a level-set approach. With this approach, the state constraints can be managed through an exact penalization technique. |
| first_indexed | 2024-10-01T07:17:08Z |
| format | Journal Article |
| id | ntu-10356/143416 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:17:08Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1434162023-02-28T19:50:42Z A level-set approach for stochastic optimal control problems under controlled-loss constraints Bouveret, Geraldine Picarelli, Athena School of Physical and Mathematical Sciences Science::Mathematics Optimal Control Viscosity Solutions 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 additional strong assumptions on the dynamics of the processes involved and the set of constraints. To treat this problem in absence of those assumptions, we first convert it into a state-constrained stochastic target problem and then apply a level-set approach. With this approach, the state constraints can be managed through an exact penalization technique. Accepted version Authors are grateful to the Young Investigator Training Program and Association of Bank Foundations. This is a post-peer-review, pre-copyedit version of an article published in Journal of Optimization Theory and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10957-020-01724-8 2020-08-31T06:07:10Z 2020-08-31T06:07:10Z 2020 Journal Article Bouveret, G., & Picarelli, A. (2020). A level-set approach for stochastic optimal control problems under controlled-loss constraints. Journal of Optimization Theory and Applications. doi:10.1007/s10957-020-01724-8 0022-3239 https://hdl.handle.net/10356/143416 10.1007/s10957-020-01724-8 en Journal of Optimization Theory and Applications © 2020 Springer Nature Switzerland AG. This is a post-peer-review, pre-copyedit version of an article published in Journal of Optimization Theory and Applications. The final authenticated version is available online at https://doi.org/10.1007/s10957-020-01724-8 application/pdf |
| spellingShingle | Science::Mathematics Optimal Control Viscosity Solutions Bouveret, Geraldine Picarelli, Athena A level-set approach for stochastic optimal control problems under controlled-loss constraints |
| title | A level-set approach for stochastic optimal control problems under controlled-loss constraints |
| title_full | A level-set approach for stochastic optimal control problems under controlled-loss constraints |
| title_fullStr | A level-set approach for stochastic optimal control problems under controlled-loss constraints |
| title_full_unstemmed | A level-set approach for stochastic optimal control problems under controlled-loss constraints |
| title_short | A level-set approach for stochastic optimal control problems under controlled-loss constraints |
| title_sort | level set approach for stochastic optimal control problems under controlled loss constraints |
| topic | Science::Mathematics Optimal Control Viscosity Solutions |
| url | https://hdl.handle.net/10356/143416 |
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