Non-local Hamilton-Jacobi-Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908610390392832 |
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| author | Bandini, Elena Keller, Christian |
| author_facet | Bandini, Elena Keller, Christian |
| contents | We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local path-dependent Hamilton-Jacobi-Bellman equation. This is the first well-posedness result for nonsmooth solutions of fully nonlinear non-local path-dependent partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-local Hamilton-Jacobi-Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes Bandini, Elena Keller, Christian Probability Analysis of PDEs Optimization and Control 45K05, 35D99, 49L20, 90C40, 93E20 We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local path-dependent Hamilton-Jacobi-Bellman equation. This is the first well-posedness result for nonsmooth solutions of fully nonlinear non-local path-dependent partial differential equations. |
| title | Non-local Hamilton-Jacobi-Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes |
| topic | Probability Analysis of PDEs Optimization and Control 45K05, 35D99, 49L20, 90C40, 93E20 |
| url | https://arxiv.org/abs/2408.02147 |