An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix
This paper studies a general class of time-inconsistent stochastic control problems under ambiguous covariance matrix. The time inconsistency is caused in various ways by a general objective functional and thus the associated control problem does not admit Bellman’s principle of optimality. Moreover...
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| Format: | Journal Article |
| Language: | English |
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2024
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| Online Access: | https://hdl.handle.net/10356/173049 |
| _version_ | 1826128428446777344 |
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| author | Lei, Qian Pun, Chi Seng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Lei, Qian Pun, Chi Seng |
| author_sort | Lei, Qian |
| collection | NTU |
| description | This paper studies a general class of time-inconsistent stochastic control problems under ambiguous covariance matrix. The time inconsistency is caused in various ways by a general objective functional and thus the associated control problem does not admit Bellman’s principle of optimality. Moreover, we model the state by a McKean–Vlasov dynamics under a set of non-dominated probability measures induced by the ambiguous covariance matrix of the noises. We apply a game-theoretic concept of subgame perfect Nash equilibrium to develop a robust equilibrium control approach, which can yield robust time-consistent decisions. We characterize the robust equilibrium control and equilibrium value function by an extended optimality principle and then we further deduce a system of Bellman–Isaacs equations to determine the equilibrium solution on the Wasserstein space of probability measures. The proposed analytical framework is illustrated with its applications to robust continuous-time mean-variance portfolio selection problems with risk aversion coefficient being constant or state-dependent, under the ambiguity stemming from ambiguous volatilities of multiple assets or ambiguous correlation between two risky assets. The explicit equilibrium portfolio solutions are represented in terms of the probability law. |
| first_indexed | 2024-10-01T07:24:49Z |
| format | Journal Article |
| id | ntu-10356/173049 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:24:49Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1730492024-01-15T15:35:49Z An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix Lei, Qian Pun, Chi Seng School of Physical and Mathematical Sciences Science::Mathematics Dynamic Programming/optimal Control Time Inconsistency This paper studies a general class of time-inconsistent stochastic control problems under ambiguous covariance matrix. The time inconsistency is caused in various ways by a general objective functional and thus the associated control problem does not admit Bellman’s principle of optimality. Moreover, we model the state by a McKean–Vlasov dynamics under a set of non-dominated probability measures induced by the ambiguous covariance matrix of the noises. We apply a game-theoretic concept of subgame perfect Nash equilibrium to develop a robust equilibrium control approach, which can yield robust time-consistent decisions. We characterize the robust equilibrium control and equilibrium value function by an extended optimality principle and then we further deduce a system of Bellman–Isaacs equations to determine the equilibrium solution on the Wasserstein space of probability measures. The proposed analytical framework is illustrated with its applications to robust continuous-time mean-variance portfolio selection problems with risk aversion coefficient being constant or state-dependent, under the ambiguity stemming from ambiguous volatilities of multiple assets or ambiguous correlation between two risky assets. The explicit equilibrium portfolio solutions are represented in terms of the probability law. Ministry of Education (MOE) Submitted/Accepted version Funding was provided by Ministry of Education - Singapore (Grant No. MOE-T2EP20220-0013). 2024-01-10T05:26:58Z 2024-01-10T05:26:58Z 2023 Journal Article Lei, Q. & Pun, C. S. (2023). An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix. Applied Mathematics and Optimization, 88(3), 91-. https://dx.doi.org/10.1007/s00245-023-10069-3 0095-4616 https://hdl.handle.net/10356/173049 10.1007/s00245-023-10069-3 2-s2.0-85174743917 3 88 91 en MOE-T2EP20220-0013 Applied Mathematics and Optimization © 2023 The Author(s), under exclusive licence to Springer Science Business Media, LLC, part of Springer Nature. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1007/s00245-023-10069-3. application/pdf |
| spellingShingle | Science::Mathematics Dynamic Programming/optimal Control Time Inconsistency Lei, Qian Pun, Chi Seng An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix |
| title | An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix |
| title_full | An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix |
| title_fullStr | An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix |
| title_full_unstemmed | An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix |
| title_short | An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix |
| title_sort | extended mckean vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix |
| topic | Science::Mathematics Dynamic Programming/optimal Control Time Inconsistency |
| url | https://hdl.handle.net/10356/173049 |
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