Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2018; 55(2): 561-572

Online first article January 9, 2018      Printed March 30, 2018

https://doi.org/10.4134/BKMS.b170151

Copyright © The Korean Mathematical Society.

Statistical causality and extremal measures

Ljiljana Petrovi\' c, Dragana Valjarevi\' c

University of Belgrade, University of Kosovska Mitrovica

Abstract

In this paper we consider the concept of statistical causality in continuous time between flows of information, represented by filtrations. Then we relate the given concept of causality to the equivalent change of measure that plays an important role in mathematical finance. We give necessary and sufficient 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.

Keywords: filtration, Granger's causality, extremal measure, equivalent martingale measure

MSC numbers: Primary 60G44; Secondary 60H07, 60H10, 62P20

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