Optimal stopping with random exercise lag

We study optimal stopping with exponentially distributed exercise lag. We formalize the problem first in a general Markovian setting and derive a set of conditions under which the solution exists. In particular, no semicontinuity assumptions of the payoff function are needed. We analyze also some specific classes of lagged optimal stopping problems with one‐dimensional diffusion dynamics where the solution can be characterized in closed form. Finally, the results are illustrated with an explicit example.