On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift

We investigate properties of processes Xt which are weak solutions of multidimensional stochastic differential equations of the formdXt=b(t,Xt) dt+dWt.We show that under certain non-stochastic conditions the solution Xt itself satisfies a uniform Novikov property. Consequently, it will follow that under these assumptions the no arbitrage property of Xt can be obtained by applying the Girsanov theorem twice (in reverse directions). For the sake of illustration, some examples with exploding drifts b are presented.