Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps
<p style="text-align:justify;">We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems, piecewise consta...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Springer Nature
2019
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| _version_ | 1826266409483632640 |
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| author | Dumitrescu, R Reisinger, C Zhang, Y |
| author_facet | Dumitrescu, R Reisinger, C Zhang, Y |
| author_sort | Dumitrescu, R |
| collection | OXFORD |
| description | <p style="text-align:justify;">We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems, piecewise constant policy timestepping reduces the problem to nonlocal semi-linear equations with different control parameters, uncoupled over individual time steps, which we solve by fully implicit monotone approximations to the controlled diffusion and the nonlocal term, and specifically the Lax–Friedrichs scheme for the nonlinearity in the gradient. We establish a comparison principle for the switching system and demonstrate the convergence of the schemes, which subsequently gives a constructive proof for the existence of a solution to the switching system. Numerical experiments are presented for a recursive utility maximization problem to demonstrate the effectiveness of the new schemes.</p> |
| first_indexed | 2024-03-06T20:38:30Z |
| format | Journal article |
| id | oxford-uuid:3370f610-d151-4920-8435-f5d90b5a34d5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:38:30Z |
| publishDate | 2019 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | oxford-uuid:3370f610-d151-4920-8435-f5d90b5a34d52022-03-26T13:20:21ZApproximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumpsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3370f610-d151-4920-8435-f5d90b5a34d5EnglishSymplectic Elements at OxfordSpringer Nature2019Dumitrescu, RReisinger, CZhang, Y <p style="text-align:justify;">We propose a class of numerical schemes for mixed optimal stopping and control of processes with infinite activity jumps and where the objective is evaluated by a nonlinear expectation. Exploiting an approximation by switching systems, piecewise constant policy timestepping reduces the problem to nonlocal semi-linear equations with different control parameters, uncoupled over individual time steps, which we solve by fully implicit monotone approximations to the controlled diffusion and the nonlocal term, and specifically the Lax–Friedrichs scheme for the nonlinearity in the gradient. We establish a comparison principle for the switching system and demonstrate the convergence of the schemes, which subsequently gives a constructive proof for the existence of a solution to the switching system. Numerical experiments are presented for a recursive utility maximization problem to demonstrate the effectiveness of the new schemes.</p> |
| spellingShingle | Dumitrescu, R Reisinger, C Zhang, Y Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps |
| title | Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps |
| title_full | Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps |
| title_fullStr | Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps |
| title_full_unstemmed | Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps |
| title_short | Approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps |
| title_sort | approximation schemes for mixed optimal stopping and control problems with nonlinear expectations and jumps |
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