Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation

Dragana Valjarević ()
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Dragana Valjarević: Department of Mathematics, Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia

Mathematics, 2024, vol. 12, issue 5, 1-11

Abstract: The paper considers the statistical concept of causality in continuous time, which is based on Granger’s definition of causality. We give necessary and sufficient conditions, in terms of statistical causality, for the preservation of the strong property of predictable representation for stopped martingales when filtration is decreased. This concept of causality is also connected to the preservation of the strong property of predictable representation under a change in measure. In addition, we give conditions, in terms of statistical causality, for martingales to have strong and weak properties of predictable representation. The results are applied to the problem of pricing claims in incomplete financial markets.

Keywords: filtration; statistical causality; strong property of predictable representation; stopped martingale (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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