| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 48 | |
| Number of page(s) | 42 | |
| DOI | https://doi.org/10.1051/cocv/2024036 | |
| Published online | 11 June 2024 | |
Linear-quadratic stochastic volterra controls II. Optimal strategies and Riccati-Volterra equations
1
Department of Mathematics, Kyoto University,
Kyoto
606-8502,
Japan
2
School of Mathematics, Sichuan University.
Chengdu,
PR China
* Corresponding author: hmgch2950@gmail.com
Received:
25
July
2023
Accepted:
12
April
2024
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.
Mathematics Subject Classification: 60H20 / 45A05 / 93E20 / 93B52
Key words: Linear-quadratic control / stochastic Volterra integral equation / Riccati–Volterra equation
© The authors. Published by EDP Sciences, SMAI 2024
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