Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems
In N. V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value functions of controlled diffusion processes can be approximated with order 1/6...
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| Format: | Journal article |
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Institute of Mathematical Statistics
2019
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| _version_ | 1797058323909967872 |
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| author | Reisinger, C Jakobsen, E Picarelli, A |
| author_facet | Reisinger, C Jakobsen, E Picarelli, A |
| author_sort | Reisinger, C |
| collection | OXFORD |
| description | In N. V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value functions of controlled diffusion processes can be approximated with order 1/6 error by those with controls which are constant on uniform time intervals. In this note we refine the proof and show that the provable rate can be improved to 1/4, which is optimal in our setting. Moreover, we demonstrate the improvements this implies for error estimates derived by similar techniques for approximation schemes, bringing these in line with the best available results from the PDE literature. |
| first_indexed | 2024-03-06T19:48:52Z |
| format | Journal article |
| id | oxford-uuid:2345aea7-a508-44c0-8797-849078939f0d |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:48:52Z |
| publishDate | 2019 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:2345aea7-a508-44c0-8797-849078939f0d2022-03-26T11:43:31ZImproved order 1/4 convergence for piecewise constant policy approximation of stochastic control problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2345aea7-a508-44c0-8797-849078939f0dSymplectic Elements at OxfordInstitute of Mathematical Statistics2019Reisinger, CJakobsen, EPicarelli, AIn N. V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piece-wise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value functions of controlled diffusion processes can be approximated with order 1/6 error by those with controls which are constant on uniform time intervals. In this note we refine the proof and show that the provable rate can be improved to 1/4, which is optimal in our setting. Moreover, we demonstrate the improvements this implies for error estimates derived by similar techniques for approximation schemes, bringing these in line with the best available results from the PDE literature. |
| spellingShingle | Reisinger, C Jakobsen, E Picarelli, A Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems |
| title | Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems |
| title_full | Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems |
| title_fullStr | Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems |
| title_full_unstemmed | Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems |
| title_short | Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems |
| title_sort | improved order 1 4 convergence for piecewise constant policy approximation of stochastic control problems |
| work_keys_str_mv | AT reisingerc improvedorder14convergenceforpiecewiseconstantpolicyapproximationofstochasticcontrolproblems AT jakobsene improvedorder14convergenceforpiecewiseconstantpolicyapproximationofstochasticcontrolproblems AT picarellia improvedorder14convergenceforpiecewiseconstantpolicyapproximationofstochasticcontrolproblems |