Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle
This paper introduces an innovative framework for dynamically optimizing consumption and investment decisions by integrating a risk penalization mechanism directly into the system’s dynamics. Leveraging Forward-Backward Stochastic Differential Equations (FBSDEs), our approach enables adaptive risk...
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| Format: | Article |
| Language: | English |
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Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila
2025-07-01
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| Series: | Journal of Innovative Applied Mathematics and Computational Sciences |
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| Online Access: | https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1950 |
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| author | Kayembe Tcheick Mubenga Kamputo Pascal Bofeki Bosonga Eugene Mbuyi Mukendi |
| author_facet | Kayembe Tcheick Mubenga Kamputo Pascal Bofeki Bosonga Eugene Mbuyi Mukendi |
| author_sort | Kayembe Tcheick |
| collection | DOAJ |
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This paper introduces an innovative framework for dynamically optimizing consumption and investment decisions by integrating a risk penalization mechanism directly into the system’s dynamics. Leveraging Forward-Backward Stochastic Differential Equations (FBSDEs), our approach enables adaptive risk regulation in response to market fluctuations. We formulate the optimization problem, analyze the associated adjoint equations, and derive explicit characterizations of optimal strategies. Numerical simulations across multiple scenarios validate the robustness of the proposed method, demonstrating a significant reduction in terminal wealth variance compared to classical approaches. Our model thus offers a promising advance in dynamic financial risk management.
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| format | Article |
| id | doaj-art-c5ecf49694ab4aff96f7bca9bb0e2880 |
| institution | Kabale University |
| issn | 2773-4196 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Institute of Sciences and Technology, University Center Abdelhafid Boussouf, Mila |
| record_format | Article |
| series | Journal of Innovative Applied Mathematics and Computational Sciences |
| spelling | doaj-art-c5ecf49694ab4aff96f7bca9bb0e28802025-08-20T03:32:16ZengInstitute of Sciences and Technology, University Center Abdelhafid Boussouf, MilaJournal of Innovative Applied Mathematics and Computational Sciences2773-41962025-07-015110.58205/jiamcs.v5i1.1950Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principleKayembe Tcheick0https://orcid.org/0009-0008-2125-5463Mubenga Kamputo Pascal1https://orcid.org/0009-0005-1440-5556Bofeki Bosonga 2Eugene Mbuyi Mukendi 3https://orcid.org/0009-0008-0200-305XUniversité de KinshasaUniversity of KinshasaUniversity of KinshasaUniversity of Kinshasa This paper introduces an innovative framework for dynamically optimizing consumption and investment decisions by integrating a risk penalization mechanism directly into the system’s dynamics. Leveraging Forward-Backward Stochastic Differential Equations (FBSDEs), our approach enables adaptive risk regulation in response to market fluctuations. We formulate the optimization problem, analyze the associated adjoint equations, and derive explicit characterizations of optimal strategies. Numerical simulations across multiple scenarios validate the robustness of the proposed method, demonstrating a significant reduction in terminal wealth variance compared to classical approaches. Our model thus offers a promising advance in dynamic financial risk management. https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1950Dynamic Risk Penalization ; Dynamic Optimization ; Portfolio Management ; Stochastic Control |
| spellingShingle | Kayembe Tcheick Mubenga Kamputo Pascal Bofeki Bosonga Eugene Mbuyi Mukendi Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle Journal of Innovative Applied Mathematics and Computational Sciences Dynamic Risk Penalization ; Dynamic Optimization ; Portfolio Management ; Stochastic Control |
| title | Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle |
| title_full | Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle |
| title_fullStr | Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle |
| title_full_unstemmed | Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle |
| title_short | Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin's principle |
| title_sort | optimal control via fbsde with dynamic risk penalization a structuring formulation based on pontryagin s principle |
| topic | Dynamic Risk Penalization ; Dynamic Optimization ; Portfolio Management ; Stochastic Control |
| url | https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/1950 |
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