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arXiv · 1704.03430

Stochastic control of mean-field SPDEs with jumps

Roxana Dumitrescu·Bernt Øksendal·Agnès Sulem
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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.

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Roxana Dumitrescu, Bernt Øksendal, Agnès Sulem. 2017-04-11. Stochastic control of mean-field SPDEs with jumps. https://arxiv.org/abs/1704.03430

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