Stochastic control of mean-field SPDEs with jumps
Abstract
We study the problem of optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in the case of \textit{partial information} control. One important novelty of our problem is represented by the introduction of \textit{general mean-field} operators, acting on both the controlled state process and the control process. We first formulate a sufficient and a necessary maximum principle for this type of control. We then prove existence and uniqueness of the solution of such general forward and backward mean-field stochastic partial differential equations. We finally apply our results to find the explicit optimal control for an optimal harvesting problem.
Keywords
Cite
@article{arxiv.1704.03430,
title = {Stochastic control of mean-field SPDEs with jumps},
author = {Roxana Dumitrescu and Bernt Øksendal and Agnès Sulem},
journal= {arXiv preprint arXiv:1704.03430},
year = {2017}
}