Before revision:  In particular, for one dimensional Markov switching models we provide sufficient and necessary conditions for the existence of structure preserving equivalent (local) martingale measures. Mathematically, our proofs are based on local changes of measures and existence and uniqueness conditions .
After revision:  In particular, for one dimensional Markov switching models the minimal martingale measure preserves the independence of the noise and we study how the minimal martingale measure can be modified to change the structure of the switching mechanism. Our main mathematical tools are new criteria for the martingale and strict local martingale property of certain stochastic exponentials .