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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