BSDE with Jumps When Mean Reflection Is Nonlinear
In this paper, we investigate a reflected backward stochastic differential equation (RBSDE) with jumps, focusing on cases where the mean reflection is nonlinear. Unlike traditional RBSDEs, this particular type of RBSDE imposes a constraint defined by the mean of a loss function that does not follow...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/9963889 |
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| _version_ | 1832546143170461696 |
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| author | Winfrida Felix Mwigilwa Farai Julius Mhlanga |
| author_facet | Winfrida Felix Mwigilwa Farai Julius Mhlanga |
| author_sort | Winfrida Felix Mwigilwa |
| collection | DOAJ |
| description | In this paper, we investigate a reflected backward stochastic differential equation (RBSDE) with jumps, focusing on cases where the mean reflection is nonlinear. Unlike traditional RBSDEs, this particular type of RBSDE imposes a constraint defined by the mean of a loss function that does not follow the continuous condition. We start by deriving an a priori estimate of the solution, followed by establishing the uniqueness and existence of the solution. Theoretical results are illustrated by way of an example of the application of super-hedging to the reinsurance and investment problem under a risk constraint. |
| format | Article |
| id | doaj-art-834ba9c5591d45949a8911bdab75a781 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-834ba9c5591d45949a8911bdab75a7812025-02-03T07:23:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/9963889BSDE with Jumps When Mean Reflection Is NonlinearWinfrida Felix Mwigilwa0Farai Julius Mhlanga1Department of Computer Systems and MathematicsDepartment of Mathematics and Applied MathematicsIn this paper, we investigate a reflected backward stochastic differential equation (RBSDE) with jumps, focusing on cases where the mean reflection is nonlinear. Unlike traditional RBSDEs, this particular type of RBSDE imposes a constraint defined by the mean of a loss function that does not follow the continuous condition. We start by deriving an a priori estimate of the solution, followed by establishing the uniqueness and existence of the solution. Theoretical results are illustrated by way of an example of the application of super-hedging to the reinsurance and investment problem under a risk constraint.http://dx.doi.org/10.1155/2024/9963889 |
| spellingShingle | Winfrida Felix Mwigilwa Farai Julius Mhlanga BSDE with Jumps When Mean Reflection Is Nonlinear International Journal of Mathematics and Mathematical Sciences |
| title | BSDE with Jumps When Mean Reflection Is Nonlinear |
| title_full | BSDE with Jumps When Mean Reflection Is Nonlinear |
| title_fullStr | BSDE with Jumps When Mean Reflection Is Nonlinear |
| title_full_unstemmed | BSDE with Jumps When Mean Reflection Is Nonlinear |
| title_short | BSDE with Jumps When Mean Reflection Is Nonlinear |
| title_sort | bsde with jumps when mean reflection is nonlinear |
| url | http://dx.doi.org/10.1155/2024/9963889 |
| work_keys_str_mv | AT winfridafelixmwigilwa bsdewithjumpswhenmeanreflectionisnonlinear AT faraijuliusmhlanga bsdewithjumpswhenmeanreflectionisnonlinear |