  In this paper we consider stopping problems for continuous-time Markov chains
under a general risk-sensitive optimization criterion for problems with finite
and infinite time horizon. More precisely our aim is to maximize the certainty
equivalent of the stopping reward minus cost over the time horizon. We derive
optimality equations for the value functions and prove the existence of optimal
stopping times. The exponential utility is treated as a special case. In
contrast to risk-neutral stopping problems it may be optimal to stop between
jumps of the Markov chain. We briefly discuss the influence of the risk
sensitivity on the optimal stopping time and consider a special house selling
problem as an example.
