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Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps

Author

Listed:
  • Roxana Dumitrescu

    (King’s College London)

  • Bernt Øksendal

    (University of Oslo)

  • Agnès Sulem

    (INRIA Paris, MathRisk research group)

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.

Suggested Citation

  • Roxana Dumitrescu & Bernt Øksendal & Agnès Sulem, 2018. "Stochastic Control for Mean-Field Stochastic Partial Differential Equations with Jumps," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 559-584, March.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:3:d:10.1007_s10957-018-1243-3
    DOI: 10.1007/s10957-018-1243-3
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    References listed on IDEAS

    as
    1. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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