In this paper we are concerned with a class of stochastic Volterra integro-dierential problems with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods. The application to optimal control provide other interesting result and require a precise descriprion of the properties of the generated semigroup. The rst main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The main technical point consists in the dierentiability of the BSDE associated with the reformulated equation with respect to its initial datum x.
|Titolo:||Feedback optimal control for stochastic Volterra equations with completely monotone kernels.|
|Data di pubblicazione:||2015|
|Appare nelle tipologie:||01.1 Articolo in Rivista|
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|Feedback Optimalcontr Volterra eq compl-monotone-kernel .pdf||Articolo principale||Post-print||Accesso riservato|