Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

We study the welfare function and the optimal control of the phosphorus deposition for the shallow lake problem with multiplicative noise. We show that the welfare function is the viscosity solution of the associated Bellman equation and we establish several properties including its asymptotic behaviour at infinity. Finally we examine the trajectories of the optimally controlled lake.