| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 34 | |
| Number of page(s) | 49 | |
| DOI | https://doi.org/10.1051/cocv/2023032 | |
| Published online | 11 May 2023 | |
The maximum principle for discounted optimal control of partially observed forward-backward stochastic systems with jumps on infinite horizon*
School of Mathematics, Shandong University, Jinan 250100, PR China
** Corresponding author: shijingtao@sdu.edu.cn
Received:
7
January
2022
Accepted:
21
April
2023
This paper is concerned with a discounted optimal control problem of partially observed forward-backward stochastic systems with jumps on infinite horizon. The control domain is convex and a kind of infinite horizon observation equation is introduced. The uniquely solvability of infinite horizon forward (backward) stochastic differential equation with jumps is obtained and more extended analyses, especially for the backward case, are made. Some new estimates are first given and proved for the critical variational inequality. Then a maximum principle is obtained by introducing some infinite horizon adjoint equations whose uniquely solvabilities are guaranteed necessarily. Finally, some comparisons are made with two kinds of representative infinite horizon stochastic systems and their related optimal controls.
Mathematics Subject Classification: 93E20 / 49K45 / 49N10 / 49N70 / 60H10
Key words: Partially observed maximum principle / infinite horizon forward-backward stochastic differential equation with jumps / discounted optimal control
© The authors. Published by EDP Sciences, SMAI 2023
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