On the Existence of Equivalent Tau-Measures in Finite Discrete Time

Suppose that (X(n)) is a finite adapted sequence of d-dimensional random variables defined on some filtered probability space ( Omega, F, ( Fn),P ) . We obtain conditions which are necessary and sufficient for the existence of a probability measure Q equivalent to P ( which we call an equivalent pi-measure ) such that each of the d component sequences of (X(n)) has a prescibed martingale property w.r.t. Q ( i.e., it is either a Q-martingale, o Q-sub- or a Q-supermartingale). This extends a version of the Fundamental Theorem of Asset Pricing due to Dalang, Morton and Willinger (1990).