A Combined Model of Classical and Impulse Controls for Emission and Stock Abatement Policies∗

This paper investigates emission and stock abatement policy decisions by the use of a stochastic optimal control model with a continuous-time setting. Environmental policies are typically referred as emission flow abatement (reduction) activities and thus, can be formulated as classical optimal control problems. However, because of recent shifts in the focus of policy measures, it is getting recognized that direct control of stock variables is also possible. To formulate such direct stock control in the framework of stochastic optimal control theory, an advanced form of control, called impulse control, is necessary. The purpose of the paper is to develop a model that combines classical flow control and impulse control, and to examine its mathematical features to obtain some policy implications.