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Stochastic control for mean-field Stochastic Partial Differential Equations with jumps

Roxana Dumitrescu 1 Bernt Øksendal 2 Agnès Sulem 3
3 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
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.
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https://hal.inria.fr/hal-01527225
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Roxana Dumitrescu, Bernt Øksendal, Agnès Sulem. Stochastic control for mean-field Stochastic Partial Differential Equations with jumps. Journal of Optimization Theory and Applications, Springer Verlag, 2018, pp 559-584. ⟨10.1007/s10957-018-1243-3⟩. ⟨hal-01527225⟩

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