| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 30 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2025020 | |
| Published online | 31 March 2025 | |
Existence of optimal controls for stochastic Volterra equations
1
Universidad del Rosario, Calle 12C No. 4-69, Bogotá, Colombia
2
Université Paris-Saclay, CNRS, ENSIIE, Univ Evry, Laboratoire de Mathématiques et Modélisation d’Evry (LaMME), 23 Boulevard de France, 91037 Evry-Courcouronnes, France
* Corresponding author: rafael.serrano@urosario.edu.co
Received:
3
February
2024
Accepted:
11
February
2025
We provide sufficient conditions that guarantee the existence of relaxed optimal controls in the weak formulation of control problems for stochastic Volterra equations (SVEs). Our study can be applied when the kernel appearing in the controlled SVE is singular at zero. The existence of relaxed optimal policies relies on the interaction between integrability hypotheses on the kernel and growth conditions on the running cost functional and the coefficients of the controlled SVEs. Under classical convexity assumptions, we can also deduce the existence of optimal strict controls.
Mathematics Subject Classification: 93E20 / 60G22 / 60H20
Key words: Stochastic Volterra equations / convolution kernel / singular fractional kernel / relaxed control / Young measures / tightness / weak formulation
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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