On the existence of equivalent [tau]-measures in finite discrete time

Klaus Schürger

Stochastic Processes and their Applications, 1996, vol. 61, issue 1, 109-128

Abstract: 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 [tau]-measure) such that each of the d component sequences of (X(n)) has a prescribed martingale property w.r.t. Q (i.e., it is either a Q-martingale, a Q-sub- or a Q-supermartingale). This extends a version of the Fundamental Theorem of Asset Pricing due to Dalang et al. (1990).

Keywords: Equivalent martingale measure No-arbitrage; Security market (search for similar items in EconPapers)
Date: 1996
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