In discrete time a local martingale is a martingale under an equivalent probability measure
The author formulates and proves the following result. Let a discrete-time infinite horizon model with an adapted \(d\)-dimensional process \(S\) be considered. If \(S\) is a local martingale on some stochastic basis, then there exists an equivalent probability measure under which \(S\) is a martingale with respect to the same filtration. The proof uses an approach originating from geometric functional analysis. It is based on separation arguments in an ingeniously chosen countably-normed space where the separating functional happens to be the density of the desired martingale measure. The most involved part of the proof is to verify the conditions of the Krein-Šchmulian theorem.
scientific article; zbMATH DE number 5520646