OPTIMAL HARVESTING AND PLANTING CONTROL IN STOCHASTIC LOGISTIC POPULATION MODELS

We consider the optimal harvesting and planting control problem to maximize the expected total net benefits in the stochastic logistic population model. The variational inequality associated with this problem is given by the degenerate form of elliptic type with quadratic coefficients. Using the viscosity solutions technique, we solve the corresponding penalty equation and show the existence of a solution to the variational inequality. The optimal harvesting and planting policy is characterized in terms of two thresholds for the variational inequality.