  This paper introduces a new class of optimal switching problems, where the
player is allowed to switch at a sequence of exogenous Poisson arrival times,
and the underlying switching system is governed by an infinite horizon backward
stochastic differential equation system. The value function and the optimal
switching strategy are characterized by the solution of the underlying
switching system. In a Markovian setting, the paper gives a complete
description of the structure of switching regions by means of the comparison
principle.
