Optimal firm behavior under pollution irreversibility risk, and distance to irreversibility thresholds

We study optimal firm behavior under irreversible pollution risk for a general class of models with irreversible local pollution. Irreversibility comes from the decay rate of pollution dropping to zero above a pollution level featuring non-convexity. In addition, the firm can instantaneously move from a reversible to an irreversible pollution mode, following a Poisson process. First, we prove for the general class of models that for any value of the Poisson probability, the optimal emission policy leads to more pollution with the irreversibility risk than without in a neighborhood of the irreversibility threshold. It's shown that the extent of uncertainty (as captured by the Poisson arrival rate) is second-order in this neighborhood. Next we study the robustness of the latter result at any pollution level in the case of linear-quadratic objective functions. We find that the general local result does not necessarily hold if actual pollution is far enough from the irreversibility threshold.