Statistical causality and martingale representation property with application to stochastic differential equations

Authors

  • L. Petrović Faculty of Economics, University of Belgrade
  • D. Valjarevic Faculty of Science, University of Kosovska Mitrovica

Keywords:

Filtrations, causality, representation property, semimartingale, stochastic differential equations

Abstract

The paper considers a statistical concept of causality in continuous time between filtered probability spaces, based on Granger’s definition of causality. This causality concept is connected with the preservation of the martingale representation property when the filtration is getting smaller. We also give conditions, in terms of causality, for every martingale to be a continuous semimartingale, and we consider the equivalence between the concept of causality and the preservation of the martingale representation property under change of measure. In addition, we apply these results to weak solutions of stochastic differential equations. The results can be applied to the economics of securities trading. DOI: 10.1017/S000497271400029X

Author Biography

D. Valjarevic, Faculty of Science, University of Kosovska Mitrovica

Department of Mathematics

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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