Jukka Lempa: Optimal Stopping with Random Exercise Lag

We discuss the following non-standard optimal stopping problem. The decision maker follows the underlying process and is free to choose the stopping time based on the observed information. On the time of stopping, the payoff is not settled immediately but after an independent exponentially distributed waiting time. Decision makers objective is to maximize the expected present value of the exercise payoff subject to the exercise lag. We discuss some general properties of the solution to this problem in a fairly general Markovian setting.