Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps
The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite. The notion of closed-loop strategies is introduced,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-11-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/21/4062 |
| _version_ | 1797467369903226880 |
|---|---|
| author | Zixuan Li Jingtao Shi |
| author_facet | Zixuan Li Jingtao Shi |
| author_sort | Zixuan Li |
| collection | DOAJ |
| description | The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite. The notion of closed-loop strategies is introduced, and the sufficient and necessary conditions for the closed-loop solvability are given. The optimal closed-loop strategy is characterized by a Riccati integral–differential equation and a backward stochastic differential equation with Poisson jumps. A simple example is given to demonstrate the effectiveness of the main result. |
| first_indexed | 2024-03-09T18:51:42Z |
| format | Article |
| id | doaj.art-365b28f73c7f498dad72e14b2515b69f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:51:42Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-365b28f73c7f498dad72e14b2515b69f2023-11-24T05:44:19ZengMDPI AGMathematics2227-73902022-11-011021406210.3390/math10214062Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson JumpsZixuan Li0Jingtao Shi1School of Mathematics, Shandong University, Jinan 250100, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaThe stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite. The notion of closed-loop strategies is introduced, and the sufficient and necessary conditions for the closed-loop solvability are given. The optimal closed-loop strategy is characterized by a Riccati integral–differential equation and a backward stochastic differential equation with Poisson jumps. A simple example is given to demonstrate the effectiveness of the main result.https://www.mdpi.com/2227-7390/10/21/4062stochastic linear–quadratic optimal controlPoisson random measurebackward stochastic differential equation with Poisson jumpsRiccati integral–differential equationclosed-loop solvability |
| spellingShingle | Zixuan Li Jingtao Shi Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps Mathematics stochastic linear–quadratic optimal control Poisson random measure backward stochastic differential equation with Poisson jumps Riccati integral–differential equation closed-loop solvability |
| title | Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps |
| title_full | Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps |
| title_fullStr | Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps |
| title_full_unstemmed | Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps |
| title_short | Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps |
| title_sort | closed loop solvability of stochastic linear quadratic optimal control problems with poisson jumps |
| topic | stochastic linear–quadratic optimal control Poisson random measure backward stochastic differential equation with Poisson jumps Riccati integral–differential equation closed-loop solvability |
| url | https://www.mdpi.com/2227-7390/10/21/4062 |
| work_keys_str_mv | AT zixuanli closedloopsolvabilityofstochasticlinearquadraticoptimalcontrolproblemswithpoissonjumps AT jingtaoshi closedloopsolvabilityofstochasticlinearquadraticoptimalcontrolproblemswithpoissonjumps |