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

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  • Dragana Valjarević

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

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.

Suggested Citation

  • Dragana Valjarević, 2024. "Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation," Mathematics, MDPI, vol. 12(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:722-:d:1348574
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    References listed on IDEAS

    as
    1. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    2. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. S. D. Jacka, 1992. "A Martingale Representation Result and an Application to Incomplete Financial Markets," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 239-250, October.
    4. Comte, F. & Renault, E., 1996. "Noncausality in Continuous Time Models," Econometric Theory, Cambridge University Press, vol. 12(2), pages 215-256, June.
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