Stochastic control for mean-field SPDEs with jumps

TY - JOUR

T1 - Stochastic control for mean-field SPDEs with jumps

AU - Dumitrescu, Roxana-Larisa

AU - Oksendal, Bernt

AU - Sulem, Agnès

PY - 2018/2/20

Y1 - 2018/2/20

N2 - 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 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 finally apply our results to find the explicit optimal control for an optimal harvesting problem.

AB - 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 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 finally apply our results to find the explicit optimal control for an optimal harvesting problem.

U2 - 10.1007/s10957-018-1243-3

DO - 10.1007/s10957-018-1243-3

M3 - Article

SN - 0022-3239

VL - 176

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -