Linear-quadratic stochastic Volterra controls I: Causal feedback strategies
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909440471465984 |
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| author | Hamaguchi, Yushi Wang, Tianxiao |
| author_facet | Hamaguchi, Yushi Wang, Tianxiao |
| contents | In this paper, we formulate and investigate the notion of causal feedback strategies arising in linear-quadratic control problems for stochastic Volterra integral equations (SVIEs) with singular and non-convolution-type coefficients. We show that there exists a unique solution, which we call the causal feedback solution, to the closed-loop system of a controlled SVIE associated with a causal feedback strategy. Furthermore, introducing two novel equations named a Type-II extended backward stochastic Volterra integral equation and a Lyapunov--Volterra equation, we prove a duality principle and a representation formula for a quadratic functional of controlled SVIEs in the framework of causal feedback strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_08333 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Linear-quadratic stochastic Volterra controls I: Causal feedback strategies Hamaguchi, Yushi Wang, Tianxiao Optimization and Control Probability 60H20, 45A05, 93E20, 93B52 In this paper, we formulate and investigate the notion of causal feedback strategies arising in linear-quadratic control problems for stochastic Volterra integral equations (SVIEs) with singular and non-convolution-type coefficients. We show that there exists a unique solution, which we call the causal feedback solution, to the closed-loop system of a controlled SVIE associated with a causal feedback strategy. Furthermore, introducing two novel equations named a Type-II extended backward stochastic Volterra integral equation and a Lyapunov--Volterra equation, we prove a duality principle and a representation formula for a quadratic functional of controlled SVIEs in the framework of causal feedback strategies. |
| title | Linear-quadratic stochastic Volterra controls I: Causal feedback strategies |
| topic | Optimization and Control Probability 60H20, 45A05, 93E20, 93B52 |
| url | https://arxiv.org/abs/2204.08333 |