Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations
An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for different control parameters. Standard convergence analysis su...
| Main Authors: | , |
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| Format: | Journal article |
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Elsevier
2016
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| _version_ | 1826301436034547712 |
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| author | Reisinger, C Forsyth, P |
| author_facet | Reisinger, C Forsyth, P |
| author_sort | Reisinger, C |
| collection | OXFORD |
| description | An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for different control parameters. Standard convergence analysis suggests that monotone (i.e., linear) interpolation must be used to transfer data between meshes. Using the equivalence to a switching system and an adaptation of the usual arguments based on consistency, stability and monotonicity, we show that if limited, potentially higher order interpolation is used for the mesh transfer, convergence is guaranteed. We provide numerical tests for the mean-variance optimal investment problem and the uncertain volatility option pricing model, and compare the results to published test cases. |
| first_indexed | 2024-03-07T05:32:24Z |
| format | Journal article |
| id | oxford-uuid:e2b5b2b6-bee6-4068-815d-cd0aac913f3a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:32:24Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:e2b5b2b6-bee6-4068-815d-cd0aac913f3a2022-03-27T10:03:28ZPiecewise constant policy approximations to Hamilton–Jacobi–Bellman equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e2b5b2b6-bee6-4068-815d-cd0aac913f3aSymplectic Elements at OxfordElsevier2016Reisinger, CForsyth, PAn advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for different control parameters. Standard convergence analysis suggests that monotone (i.e., linear) interpolation must be used to transfer data between meshes. Using the equivalence to a switching system and an adaptation of the usual arguments based on consistency, stability and monotonicity, we show that if limited, potentially higher order interpolation is used for the mesh transfer, convergence is guaranteed. We provide numerical tests for the mean-variance optimal investment problem and the uncertain volatility option pricing model, and compare the results to published test cases. |
| spellingShingle | Reisinger, C Forsyth, P Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations |
| title | Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations |
| title_full | Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations |
| title_fullStr | Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations |
| title_full_unstemmed | Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations |
| title_short | Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations |
| title_sort | piecewise constant policy approximations to hamilton jacobi bellman equations |
| work_keys_str_mv | AT reisingerc piecewiseconstantpolicyapproximationstohamiltonjacobibellmanequations AT forsythp piecewiseconstantpolicyapproximationstohamiltonjacobibellmanequations |