The optimal control of emissions and renewable resource harvesting under uncertainty

A model of a renewable resource is developed where the growth and quality of the resource are reduced by pollution. Ambient pollution concentrations and the renewable resource stock are modeled as stochastic processes. Conditions for the optimal harvest plan and the optimal emissions rate are derived. The effect of stochastic variations on the optimal management of the resource is analyzed. The steady-state joint probability distribution of the resource and pollution stocks is shown to exist under certain conditions.