Probabilistic error analysis for some approximation schemes to optimal control problems
We introduce a class of numerical schemes for optimal stochastic control problems based on a novel Markov chain approximation, which uses, in turn, a piecewise constant policy approximation, Euler–Maruyama time stepping, and a Gauß-Hermite approximation of the Gaußian increments. We provide lower er...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2020
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| _version_ | 1797103588977147904 |
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| author | Picarelli, A Reisinger, C |
| author_facet | Picarelli, A Reisinger, C |
| author_sort | Picarelli, A |
| collection | OXFORD |
| description | We introduce a class of numerical schemes for optimal stochastic control problems based on a novel Markov chain approximation, which uses, in turn, a piecewise constant policy approximation, Euler–Maruyama time stepping, and a Gauß-Hermite approximation of the Gaußian increments. We provide lower error bounds of order arbitrarily close to 1/2 in time and 1/3 in space for Lipschitz viscosity solutions, coupling probabilistic arguments with regularization techniques as introduced by Krylov. The corresponding order of the upper bounds is 1/4 in time and 1/5 in space. For sufficiently regular solutions, the order is 1 in both time and space for both bounds. Finally, we propose techniques for further improving the accuracy of the individual components of the approximation.
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| first_indexed | 2024-03-07T06:22:11Z |
| format | Journal article |
| id | oxford-uuid:f31104c8-c274-4d15-9fe2-b5d9d80636b6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:22:11Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:f31104c8-c274-4d15-9fe2-b5d9d80636b62022-03-27T12:09:09ZProbabilistic error analysis for some approximation schemes to optimal control problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f31104c8-c274-4d15-9fe2-b5d9d80636b6EnglishSymplectic Elements at OxfordElsevier2020Picarelli, AReisinger, CWe introduce a class of numerical schemes for optimal stochastic control problems based on a novel Markov chain approximation, which uses, in turn, a piecewise constant policy approximation, Euler–Maruyama time stepping, and a Gauß-Hermite approximation of the Gaußian increments. We provide lower error bounds of order arbitrarily close to 1/2 in time and 1/3 in space for Lipschitz viscosity solutions, coupling probabilistic arguments with regularization techniques as introduced by Krylov. The corresponding order of the upper bounds is 1/4 in time and 1/5 in space. For sufficiently regular solutions, the order is 1 in both time and space for both bounds. Finally, we propose techniques for further improving the accuracy of the individual components of the approximation. |
| spellingShingle | Picarelli, A Reisinger, C Probabilistic error analysis for some approximation schemes to optimal control problems |
| title | Probabilistic error analysis for some approximation schemes to optimal control problems |
| title_full | Probabilistic error analysis for some approximation schemes to optimal control problems |
| title_fullStr | Probabilistic error analysis for some approximation schemes to optimal control problems |
| title_full_unstemmed | Probabilistic error analysis for some approximation schemes to optimal control problems |
| title_short | Probabilistic error analysis for some approximation schemes to optimal control problems |
| title_sort | probabilistic error analysis for some approximation schemes to optimal control problems |
| work_keys_str_mv | AT picarellia probabilisticerroranalysisforsomeapproximationschemestooptimalcontrolproblems AT reisingerc probabilisticerroranalysisforsomeapproximationschemestooptimalcontrolproblems |