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 inESAIM. Control, optimisation and calculus of variations
Main Authors Hamaguchi, Yushi, Wang, Tianxiao
Format Journal Article
LanguageEnglish
Published 11.06.2024
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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.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2024036