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 .
We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process or a positive diffusion with Markov switching. In particular , we derive conditions for the existence of the minimal martingale measure. We also show that for 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 .
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study no arbitrage conditions for financial models in which either the stocks itself or its log returns are continuous Ito processes. More precisely
derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process or a positive diffusion with Markov switching. In particular
D
deterministic
R
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
of the minimal martingale measure. We also show that for
R
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
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