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A Filtered Version of the Bipolar Theorem of Brannath and Schachermayer

Author

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  • Gordan Žitković

    (Columbia University)

Abstract

We extend the Bipolar Theorem of Kramkov and Schachermayer(12) to the space of nonnegative càdlàg supermartingales on a filtered probability space. We formulate the notion of fork-convexity as an analogue to convexity in this setting. As an intermediate step in the proof of our main result we establish a conditional version of the Bipolar theorem. In an application to mathematical finance we describe the structure of the set of dual processes of the utility maximization problem of Kramkov and Schachermayer(12) and give a budget-constraint characterization of admissible consumption processes in an incomplete semimartingale market.

Suggested Citation

  • Gordan Žitković, 2002. "A Filtered Version of the Bipolar Theorem of Brannath and Schachermayer," Journal of Theoretical Probability, Springer, vol. 15(1), pages 41-61, January.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:1:d:10.1023_a:1013885121598
    DOI: 10.1023/A:1013885121598
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    Cited by:

    1. Bálint, Dániel Ágoston, 2022. "Characterisation of L0-boundedness for a general set of processes with no strictly positive element," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 51-75.

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