# SFB 303 Discussion Paper No. B-297

**Author:** Schürger, Klaus

**Title:** On the existence of equivalent tau-measures in finite
discrete time

**Abstract:** Suppose that (X(n)) is a finite adapted sequence
of d-dimensional random variables defined on some filtered probability
space ( Omega, F, ( F_{n}),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).

**Keywords:** equivalent martingale measure, no-arbitrage, security
market

**JEL-Classification-Number:** G12

**Creation-Date:** November 1994

**URL:**
../1994/b/bonnsfb297.pdf
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