We introduce a general framework for one- and multidimensional financial markets and study no arbitrage conditions  . More precisely, we derive deterministic conditions for the existence and nonexistence of equivalent (local) martingale measures and strict martingale densities. For continuous models with a random switching mechanism we  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. Mathematically, our proofs are based on local changes of measures and existence and uniqueness conditions.
We study no arbitrage conditions for financial models in which either the stocks itself or its log returns are continuous Ito processes . 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. Mathematically, our proofs are based on local changes of measures and existence and uniqueness conditions.
D
introduce a general framework for one- and multidimensional financial markets and
A
for financial models in which either the stocks itself or its log returns are continuous Ito processes
D
continuous
A
also