Dynamic optimisation in the presence of threshold effects when the location of the threshold is uncertain - with an application to a possible disintegration of the Western Antarctic Ice Sheet

The purpose of this paper is to derive necessary conditions for optimal control in the presence of threshold effects when the threshold is a curve in n-dimensional space of uncertain location. The usefulness of these conditions is shown by examining the optimal regulation of two greenhouse gases when there is a risk that the combined radiative forcing from these two gases may trigger the disintegration of the Western Antarctic ice sheet.