American perpetual options with random start

We consider the valuation of American perpetual options with the property that they are only possible to exercise after the occurrence of a random time, which is a stopping time with respect to a given filtration. One situation where this feature is present is when making an irreversible investment, e.g. building on vacant land, while waiting for a permit to be allowed to do so. The random time in this case is the time at which the permit is given. This and the value of a version of an abandonment option are given as two applications of this modelling framework.
QC 20191025