A Class of Finite-Dimensional Numerically Solvable McKean-Vlasov Control Problems
| Autor: | Huyên Pham, Isaque Pimentel, Alessandro Balata, Mathieu Laurière, Côme Huré |
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| Přispěvatelé: | School of Mathematics - University of Leeds, University of Leeds, Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), NYU–ECNU Institute of Mathematical Sciences at NYU Shanghai, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), School of Mathematics [Leeds] |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Polynomial control randomization ˚ 010103 numerical & computational mathematics 01 natural sciences 010104 statistics & probability McKean-Vlasov control QA1-939 FOS: Mathematics Applied mathematics Control randomization Regress later 0101 mathematics Mathematics - Optimization and Control regress-later Mathematics Stochastic control T57-57.97 Applied mathematics. Quantitative methods Markov chain Numerical analysis Quantization (signal processing) Probabilistic logic polynomial class [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Optimization and Control (math.OC) Embedding quantization [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
| Zdroj: | ESAIM: Proceedings and Surveys, Vol 65, Pp 114-144 (2019) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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