A dynamic programming approach to optimal pollution control under uncertain irreversibility: The Poisson case

We solve a bimodal optimal control problem with a non-concavity and uncertainty through a Poisson process underlying the transition from a mode to another. We use a dynamic programming approach and are able to uncover the global optimal dynamics (including optimal non-monotonic paths) under a few linear-quadratic assumptions, which do not get rid of the non-concavity of the problem. This is in contrast to the related literature on pollution control under irreversibility which usually explores local dynamics along monotonic solution paths to firstorder Pontryagin conditions.