Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional in Infinite Horizon
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909016348688384 |
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| author | Li, Lin Yong, Jiongmin |
| author_facet | Li, Lin Yong, Jiongmin |
| contents | This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of weighted $L^2$-stabilizability is introduced and characterized, which will lead to an equivalence of the optimal control problem having recursive cost functional with a classical LQ problem. Then all the results of classical problems for open-loop and closed-loop solvability of such an LQ problem can be translated, in terms of the solvability of a forward-backward stochastic differential equation and that of algebraic Riccati equation. Finally, the nonhomogeneous is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04275 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional in Infinite Horizon Li, Lin Yong, Jiongmin Optimization and Control 93E20, 49N10, 60H10 This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of weighted $L^2$-stabilizability is introduced and characterized, which will lead to an equivalence of the optimal control problem having recursive cost functional with a classical LQ problem. Then all the results of classical problems for open-loop and closed-loop solvability of such an LQ problem can be translated, in terms of the solvability of a forward-backward stochastic differential equation and that of algebraic Riccati equation. Finally, the nonhomogeneous is discussed. |
| title | Stochastic Optimal Linear Quadratic Controls with A Recursive Cost Functional in Infinite Horizon |
| topic | Optimization and Control 93E20, 49N10, 60H10 |
| url | https://arxiv.org/abs/2605.04275 |