Linear-quadratic stochastic Volterra controls II: Optimal strategies and Riccati--Volterra equations
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910762579001344 |
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| author | Hamaguchi, Yushi Wang, Tianxiao |
| author_facet | Hamaguchi, Yushi Wang, Tianxiao |
| contents | In this paper, we study linear-quadratic control problems for stochastic Volterra integral equations with singular and non-convolution-type coefficients. The weighting matrices in the cost functional are not assumed to be non-negative definite. From a new viewpoint, we formulate a framework of causal feedback strategies. The existence and the uniqueness of a causal feedback optimal strategy are characterized by means of the corresponding Riccati--Volterra equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10239 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Linear-quadratic stochastic Volterra controls II: Optimal strategies and Riccati--Volterra equations Hamaguchi, Yushi Wang, Tianxiao Optimization and Control Probability 60H20, 45A05, 93E20, 93B52 In this paper, we study linear-quadratic control problems for stochastic Volterra integral equations with singular and non-convolution-type coefficients. The weighting matrices in the cost functional are not assumed to be non-negative definite. From a new viewpoint, we formulate a framework of causal feedback strategies. The existence and the uniqueness of a causal feedback optimal strategy are characterized by means of the corresponding Riccati--Volterra equation. |
| title | Linear-quadratic stochastic Volterra controls II: Optimal strategies and Riccati--Volterra equations |
| topic | Optimization and Control Probability 60H20, 45A05, 93E20, 93B52 |
| url | https://arxiv.org/abs/2204.10239 |