Sticky processes, local and true martingales

الأصل · EN

We prove that for a so-called sticky process S there exists an equivalent probability Q and a Q-martingale S that is arbitrarily close to S in Lᵖ(Q) norm. For continuous S, S can be chosen arbitrarily close to S in supremum norm. In the case where S is a local martingale we may choose Q arbitrarily close to the original probability in the total variation norm. We provide examples to illustrate the power of our results and present applications in mathematical finance.