Infinite horizon impulse control problem with jumps and continuous switching costs
Purpose – The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Emerald Publishing
2022-01-01
|
| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-10-2020-0088/full/pdf |
| _version_ | 1797791672455659520 |
|---|---|
| author | Rim Amami Monique Pontier Hani Abidi |
| author_facet | Rim Amami Monique Pontier Hani Abidi |
| author_sort | Rim Amami |
| collection | DOAJ |
| description | Purpose – The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem. Design/methodology/approach – The main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results. Findings – In this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps. Originality/value – In this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem. |
| first_indexed | 2024-03-13T02:22:10Z |
| format | Article |
| id | doaj.art-98c8d3606ad84aef8691b306191bd45e |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-13T02:22:10Z |
| publishDate | 2022-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-98c8d3606ad84aef8691b306191bd45e2023-06-30T09:18:54ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142022-01-0128123610.1108/AJMS-10-2020-0088Infinite horizon impulse control problem with jumps and continuous switching costsRim Amami0Monique Pontier1Hani Abidi2Department of Basic Sciences, Deanship of Preparatory Year and Supporting Studies, Imam Abdulrahman Bin Faisal University, Dammam, Saudi ArabiaIMT, Paul Sabatier University, Toulouse, FranceDepartment of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, TunisiaPurpose – The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem. Design/methodology/approach – The main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results. Findings – In this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps. Originality/value – In this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.https://www.emerald.com/insight/content/doi/10.1108/AJMS-10-2020-0088/full/pdfImpulse controlInfinite horizonJumpsReflected backward stochastic differential equationsDouble barrierConstructive method of the solution |
| spellingShingle | Rim Amami Monique Pontier Hani Abidi Infinite horizon impulse control problem with jumps and continuous switching costs Arab Journal of Mathematical Sciences Impulse control Infinite horizon Jumps Reflected backward stochastic differential equations Double barrier Constructive method of the solution |
| title | Infinite horizon impulse control problem with jumps and continuous switching costs |
| title_full | Infinite horizon impulse control problem with jumps and continuous switching costs |
| title_fullStr | Infinite horizon impulse control problem with jumps and continuous switching costs |
| title_full_unstemmed | Infinite horizon impulse control problem with jumps and continuous switching costs |
| title_short | Infinite horizon impulse control problem with jumps and continuous switching costs |
| title_sort | infinite horizon impulse control problem with jumps and continuous switching costs |
| topic | Impulse control Infinite horizon Jumps Reflected backward stochastic differential equations Double barrier Constructive method of the solution |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-10-2020-0088/full/pdf |
| work_keys_str_mv | AT rimamami infinitehorizonimpulsecontrolproblemwithjumpsandcontinuousswitchingcosts AT moniquepontier infinitehorizonimpulsecontrolproblemwithjumpsandcontinuousswitchingcosts AT haniabidi infinitehorizonimpulsecontrolproblemwithjumpsandcontinuousswitchingcosts |