Abstract
We study optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in case of partial information control. One important novelty of our problem is represented by the introduction of 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 the existence and uniqueness of the solution of such general forward and backward mean-field stochastic partial differential equations. We apply our results to find the explicit optimal control for an optimal harvesting problem.
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Acknowledgements
This research was carried out with support of the Norwegian Research Council, within the research project Challenges in Stochastic Control, Information and Applications (STOCONINF), project number 250768/F20.
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Communicated by Nizar Touzi.
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Dumitrescu, R., Øksendal, B. & Sulem, A. Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps. J Optim Theory Appl 176, 559–584 (2018). https://doi.org/10.1007/s10957-018-1243-3
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DOI: https://doi.org/10.1007/s10957-018-1243-3
Keywords
- Mean-field stochastic partial differential equation
- Optimal control
- Mean-field backward stochastic partial differential equation
- Stochastic maximum principles