On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift (Q1962119)

The author investigates properties of processes \(X_t\) which are weak solutions of multidimensional stochastic differential equations of the form \(dX_t=b (t,X_t) dt+dW_t\). It is shown that, under certain non-stochastic conditions, the solution \(X_t\) itself satisfies a uniform Novikov property. Consequently, it will follow that under these assumptions the no arbitrage property of \(X_t\) can be obtained by applying the Girsanov theorem twice (in reverse direction). For the sake of illustration, some examples with exploding drifts \(b\) are presented.