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Finitely Additive Supermartingales

Author

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  • Gianluca Cassese

    (Università del Salento
    University of Lugano)

Abstract

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob–Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenous probability measure.

Suggested Citation

  • Gianluca Cassese, 2008. "Finitely Additive Supermartingales," Journal of Theoretical Probability, Springer, vol. 21(3), pages 586-603, September.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:3:d:10.1007_s10959-008-0164-8
    DOI: 10.1007/s10959-008-0164-8
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    References listed on IDEAS

    as
    1. Gianluca Cassese, 2008. "Asset Pricing With No Exogenous Probability Measure," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 23-54, January.
    2. Cassese, Gianluca, 2007. "Decomposition of supermartingales indexed by a linearly ordered set," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 795-802, April.
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