A class of finite-dimensional numerically solvable McKean-Vlasov control problems
We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stoc...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Subjects: | |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196506.pdf |
| _version_ | 1797970680819482624 |
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| author | Balata Alessandro Huré Côme Laurière Mathieu Pham Huyên Pimentel Isaque |
| author_facet | Balata Alessandro Huré Côme Laurière Mathieu Pham Huyên Pimentel Isaque |
| author_sort | Balata Alessandro |
| collection | DOAJ |
| description | We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress-later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation. |
| first_indexed | 2024-04-11T03:20:54Z |
| format | Article |
| id | doaj.art-df30f085c95a478ca0699f052fc77773 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T03:20:54Z |
| publishDate | 2019-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-df30f085c95a478ca0699f052fc777732023-01-02T09:09:22ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592019-01-016511414410.1051/proc/201965114proc196506A class of finite-dimensional numerically solvable McKean-Vlasov control problemsBalata AlessandroHuré CômeLaurière MathieuPham HuyênPimentel IsaqueWe address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be reduced by suitable Markov embedding to finite-dimensional stochastic control problems, and provide a discussion and comparison of three probabilistic numerical methods for solving the reduced control problem: quantization, regression by control randomization, and regress-later methods. Our numerical results are illustrated on various examples from portfolio selection and liquidation under drift uncertainty, and a model of interbank systemic risk with partial observation.https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196506.pdfmckean-vlasov controlpolynomial classquantizationregress-latercontrol randomization |
| spellingShingle | Balata Alessandro Huré Côme Laurière Mathieu Pham Huyên Pimentel Isaque A class of finite-dimensional numerically solvable McKean-Vlasov control problems ESAIM: Proceedings and Surveys mckean-vlasov control polynomial class quantization regress-later control randomization |
| title | A class of finite-dimensional numerically solvable McKean-Vlasov control problems |
| title_full | A class of finite-dimensional numerically solvable McKean-Vlasov control problems |
| title_fullStr | A class of finite-dimensional numerically solvable McKean-Vlasov control problems |
| title_full_unstemmed | A class of finite-dimensional numerically solvable McKean-Vlasov control problems |
| title_short | A class of finite-dimensional numerically solvable McKean-Vlasov control problems |
| title_sort | class of finite dimensional numerically solvable mckean vlasov control problems |
| topic | mckean-vlasov control polynomial class quantization regress-later control randomization |
| url | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196506.pdf |
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