Linear-quadratic stochastic Volterra controls II: Optimal strategies and Riccati--Volterra equations
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 causa...
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Published in | ESAIM. Control, optimisation and calculus of variations |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
11.06.2024
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Online Access | Get full text |
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Summary: | 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. The causal feedback optimal strategy is explicitly written by a finite dimensional (matrix-valued) function which solves the Riccati--Volterra equation. |
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ISSN: | 1292-8119 1262-3377 |
DOI: | 10.1051/cocv/2024036 |