Feedback Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels
Abstract
In this paper we are concerned with a class of stochastic Volterra integro-differential 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 first 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 differentiability of the BSDE associated with the reformulated equation with respect to its initial datum x.
Cite
@article{arxiv.1112.3818,
title = {Feedback Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels},
author = {Fulvia Confortola and Elisa Mastrogiacomo},
journal= {arXiv preprint arXiv:1112.3818},
year = {2011}
}
Comments
arXiv admin note: text overlap with arXiv:0905.3628 by different author