  This paper deals with optimal prediction in a regime-switching model driven
by a continuous-time Markov chain. We extend existing results for geometric
Brownian motion by deriving optimal stopping strategies that depend on the
current regime state, and prove a number of continuity properties relating to
optimal value and boundary functions. Our approach replaces the use of closed
form expressions, which are not available in our setting, with PDE arguments
that also simplify the approach of [2] in the classical Brownian case.
