A note on the existence of unique equivalent martingale measures in a Markovian setting

Simple sufficient conditions for the existence of a unique equivalent martingale measure are provided. Furthermore, these conditions give us a handle on situations where an equivalent martingale measure cannot exist. The existence of a unique equivalent martingale measure is of relevance to problems in mathematical finance. Two examples of models for which the question of existence was unresolved are studied. By means of our results existence of a unique equivalent measure up to an explosion time is proved.