Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls
In this research, we investigate the maximum principle pertaining to risk-sensitive optimal control problems under partial observation, modeled by forward?backward stochastic differential equations (FBSDEs) of the general regularity McKean?Vlasov form. An important aspect of these equations is that...
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Birkhauser
2025
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| author | Lakhdari I.E. Djenaihi Y. Kaouache R. Boulaaras S. Jan R. |
| author2 | 57217831964 |
| author_facet | 57217831964 Lakhdari I.E. Djenaihi Y. Kaouache R. Boulaaras S. Jan R. |
| author_sort | Lakhdari I.E. |
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| content_provider | Universiti Tenaga Nasional |
| content_source | UNITEN Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this research, we investigate the maximum principle pertaining to risk-sensitive optimal control problems under partial observation, modeled by forward?backward stochastic differential equations (FBSDEs) of the general regularity McKean?Vlasov form. An important aspect of these equations is that their coefficients are nonlinearly influenced by both the state process and its distribution. The control variable consists of two components: a continuous control and an impulse control. The cost functional is an exponential of integral type based on the regularity McKean?Vlasov framework. By applying Girsanov?s theorem and taking derivatives with respect to the probability distribution, we establish the risk-sensitive maximum principle. This principle is formulated using variational inequalities, under the assumption that the control domain is convex. Moreover, the sufficient conditions of optimality is obtained under certain concavity assumptions. As an application, the main outcomes are used to solve a linear-quadratic risk-sensitive optimal control problem of the regularity McKean?Vlasov type, both under partial and full observation conditions. ? The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. |
| format | Article |
| id | my.uniten.dspace-36136 |
| institution | Universiti Tenaga Nasional |
| publishDate | 2025 |
| publisher | Birkhauser |
| record_format | dspace |
| spelling | my.uniten.dspace-361362025-03-03T15:41:26Z Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls Lakhdari I.E. Djenaihi Y. Kaouache R. Boulaaras S. Jan R. 57217831964 57210817582 59312786200 36994353700 57205596279 In this research, we investigate the maximum principle pertaining to risk-sensitive optimal control problems under partial observation, modeled by forward?backward stochastic differential equations (FBSDEs) of the general regularity McKean?Vlasov form. An important aspect of these equations is that their coefficients are nonlinearly influenced by both the state process and its distribution. The control variable consists of two components: a continuous control and an impulse control. The cost functional is an exponential of integral type based on the regularity McKean?Vlasov framework. By applying Girsanov?s theorem and taking derivatives with respect to the probability distribution, we establish the risk-sensitive maximum principle. This principle is formulated using variational inequalities, under the assumption that the control domain is convex. Moreover, the sufficient conditions of optimality is obtained under certain concavity assumptions. As an application, the main outcomes are used to solve a linear-quadratic risk-sensitive optimal control problem of the regularity McKean?Vlasov type, both under partial and full observation conditions. ? The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Final 2025-03-03T07:41:26Z 2025-03-03T07:41:26Z 2024 Article 10.1007/s11868-024-00654-7 2-s2.0-85208739845 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85208739845&doi=10.1007%2fs11868-024-00654-7&partnerID=40&md5=b76b9ce8340cda8b410901723b792724 https://irepository.uniten.edu.my/handle/123456789/36136 15 4 82 Birkhauser Scopus |
| spellingShingle | Lakhdari I.E. Djenaihi Y. Kaouache R. Boulaaras S. Jan R. Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls |
| title | Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls |
| title_full | Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls |
| title_fullStr | Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls |
| title_full_unstemmed | Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls |
| title_short | Maximum principle for partially observed risk-sensitive optimal control problem of McKean?Vlasov FBSDEs involving impulse controls |
| title_sort | maximum principle for partially observed risk-sensitive optimal control problem of mckean?vlasov fbsdes involving impulse controls |
| url_provider | http://dspace.uniten.edu.my/ |