Before revision:  More precisely , we derive deterministic conditions for the existence and nonexistence of equivalent (local) martingale measures and strict martingale densities. For models with a random switching mechanism we also study the set of equivalent (local) martingale measures which are structure preserving. In particular, for one dimensional Markov switching models we provide sufficient and necessary conditions for the existence of structure preserving equivalent (local) martingale measures.
After revision:  More precisely , we derive deterministic conditions for the existence of the minimal martingale measure. We also show that for Markov switching models we provide sufficient and necessary conditions for the existence of structure preserving equivalent (local) martingale measures.