Optimal stopping problems for semi-Markov processes

This paper gives an overview of optimal slopping problems for continuous time semi-Markov processes. Problems of this sort arise when a decision maker is faced with the problem of finding optimal stopping or replacement rules an, for example, job-search, shock models or repair replacement models. The set-up of the paper is to provide a general framework for these sort of problems. Consequences in various submodels are also given.