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

Roxana Dumitrescu (), Bernt Øksendal () and Agnès Sulem ()
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Roxana Dumitrescu: King’s College London
Bernt Øksendal: University of Oslo
Agnès Sulem: INRIA Paris, MathRisk research group

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 3, No 3, 559-584

Abstract: 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.

Keywords: Mean-field stochastic partial differential equation; Optimal control; Mean-field backward stochastic partial differential equation; Stochastic maximum principles; 60H15; 93E20; 35R60 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1243-3

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