  In the standard models for optimal multiple stopping problems it is assumed
that between two exercises there is always a time period of deterministic
length $\delta$, the so called refraction period. This prevents the optimal
exercise times from bunching up together on top of the optimal stopping time
for the one-exercise case. In this article we generalize the standard model by
considering random refraction times. We develop the theory and reduce the
problem to a sequence of ordinary stopping problems thus extending the results
for deterministic times. This requires an extension of the underlying
filtrations in general. Furthermore we consider the Markovian case and treat an
example explicitly.
