Optimal behavior under pollution irreversibility risk and distance to the irreversibility thresholds: A global approach

We study optimal behavior under irreversible pollution risk. Irreversibility comes from the decay rate of pollution sharply dropping (possibly to zero) above a threshold pollution level. In addition, the economy can instantaneously move from a reversible to an irreversible pollution mode, following a Poisson process, the irreversible mode being an absorbing state. The resulting non-convex optimal pollution control is therefore piecewise deterministic. First, we are able to characterize analytically and globally the optimal emission policy using dynamic programming. Second, we prove 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 pollution irreversibility threshold. Third, we find that this local result does not necessarily hold if actual pollution is far enough from the irreversibility threshold. Our results enhance the importance of the avoidability of the latter threshold in the optimal economic behavior under the irreversibility risk.