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 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 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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.inria.fr/hal-01527225
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  • HAL Id : hal-01527225, version 1

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Roxana Dumitrescu, Bernt Øksendal, Agnès Sulem. Stochastic control of mean-field SPDEs with jumps. 2017. 〈hal-01527225〉

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