Statistical causality and extremal measures

Abstract

In this paper we consider the concept of statistical causality in continuous time between ows of information, represented by ltra- tions. Then we relate the given concept of causality to the equivalent change of measure that plays an important role in mathematical nance. We give necessary and sucient conditions, in terms of statistical causali- ty, for extremality of measure in the set of martingale measures. Also, we have considered the extremality of measure which involves the stopping time and the stopped processes, and obtained similar results. Finally, we show that the concept of unique equivalent martingale measure is strongly connected to the given concept of causality and apply this result to the continuous market model.