Precaution under mixed uncertainty: Implications for environmental management

A model of pollution control subject to two types of uncertainty is presented. First, the natural decay of the pollution stock follows stochastic dynamics that drives a diffusion pollution process (“stochastic uncertainty”). Moreover, the damage coefficient which determines the amount of damage corresponding to each pollution stock can undergo an abrupt increase at some uncertain future time (“event uncertainty”). The model admits an explicit and simple dynamic characterization of the optimal emission rule and the ensuing pollution process. When only one type of uncertainty is permitted (by setting either the variance of the stochastic process or the hazard rate for the damage increase to zero) it acts to promote the intuitive response of precaution. However, allowing the two types to interact gives rise to a non-monotonic behavior, whereby increasing the stochastic variance first enhances, then diminishes the response to the hazard. The results confirm and expand recent findings based on discrete-time formulations.

► We model pollution control under two types of uncertainty.
► The pollution stock follows continuous-time stochastic dynamics.
► Pollution damage may exhibit an abrupt increase at some unknown future time.
► Each type of uncertainty entails the monotonic response of increased prudence.
► The interaction between the two types implies a non-monotonic response.