When can the environmental profile and emissions reduction be optimised independently of the pollutant level?

Abstract

Consider a model for optimal timing of a policy measure which changes the emission rate, e.g. trading off the cost of reduction against the time-additive aggregate of environmental damage, the disutility from the pollutant stock the infrastructure contributes to. Intuitively, the optimal timing for an infinitesimal pollution source should reasonably not depend on its historical contribution to the stock, as this is negligible. Dropping the size assumption, we show how to reduce the minimisation problem to one not depending on the history of , under linear evolution and suitable linearity or additivity conditions on the damage functional. We employ a functional analysis framework which allows for delay equations, non-Markovian driving noise, a choice between discrete and continuous time, and a menu of integral concepts covering stochastic calculi less frequently used in resource and environmental economics. Examples are given under the common (Markovian Itô) stochastic analysis framework.