  This paper studies a general L\'evy process model of the bail-out optimal
dividend problem with an exponential time horizon, and further extends it to
the regime-switching model. We first show the optimality of a double barrier
strategy in the single-regime setting with a concave terminal payoff function.
This is then applied to show the optimality of a Markov-modulated double
barrier strategy in the regime-switching model via contraction mapping
arguments. We solve these for a general L\'evy model with both positive and
negative jumps, greatly generalizing the existing results on spectrally
one-sided models.
