Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps |
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Authors: | Roxana Dumitrescu Bernt Øksendal Agnès Sulem |
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Institution: | 1.Department of Mathematics,King’s College London,London,UK;2.Department of Mathematics,University of Oslo,Oslo,Norway;3.INRIA Paris, MathRisk research group,Paris Cedex 12,France |
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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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