2019/02/18 by Nacira Agram, Agram, Nacira, Astrid Hilbert +3
Mathematics · #60H05 #60H15 #91B70 #91G80 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:60H05 #msc:60H15 #msc:91B70 #msc:91G80 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1902.06539
arXiv admin note: text overlap with arXiv:1807.07303
arxiv created 2019/05/04 · arxiv updated 2019/05/07
We consider the problem of optimal singular control of a stochastic partial differential equation (SPDE) with space-mean dependence. Such systems are proposed as models for population growth in a random environment. We obtain sufficient and necessary maximum principles for such control problems. The corresponding adjoint equation is a reflected backward stochastic partial differential equation (BSPDE) with space-mean dependence. We prove existence and uniqueness results for such equations. As an application we study optimal harvesting from a population modelled as an SPDE with space-mean dependence.