  We develop methods to solve general optimal stopping problems with
opportunities to stop that arrive randomly. Such problems occur naturally in
applications with market frictions. Pivotal to our approach is that our methods
operate on random rather than deterministic time scales. This enables us to
convert the original problem into an equivalent discrete-time optimal stopping
problem with $\mathbb{N}_{0}$-valued stopping times and a possibly infinite
horizon. To numerically solve this problem, we design a random times least
squares Monte Carlo method. We also analyze an iterative policy improvement
procedure in this setting. We illustrate the efficiency of our methods and the
relevance of randomly arriving opportunities in a few examples.
