Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| _version_ | 1866912054290415616 |
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| author | Karoui, Nicole El Tan, Xiaolu |
| author_facet | Karoui, Nicole El Tan, Xiaolu |
| contents | We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the canonical space of paths, one can check the required measurability conditions. This covers in particular the most classical controlled/stopped diffusion processes problems. Further, we study the approximation property of the optimal control problems by piecewise constant control problems. As a byproduct, we obtain an equivalence result of the strong, weak and relaxed formulations of the controlled/stopped diffusion processes problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1310_3364 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems Karoui, Nicole El Tan, Xiaolu Optimization and Control Primary 28B20, 49L20, secondary 93E20, 60H30 We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the canonical space of paths, one can check the required measurability conditions. This covers in particular the most classical controlled/stopped diffusion processes problems. Further, we study the approximation property of the optimal control problems by piecewise constant control problems. As a byproduct, we obtain an equivalence result of the strong, weak and relaxed formulations of the controlled/stopped diffusion processes problem. |
| title | Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems |
| topic | Optimization and Control Primary 28B20, 49L20, secondary 93E20, 60H30 |
| url | https://arxiv.org/abs/1310.3364 |