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Journal of Theoretical Probability

, Volume 15, Issue 1, pp 41–61 | Cite as

A Filtered Version of the Bipolar Theorem of Brannath and Schachermayer

  • Gordan Žitković
Article

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.

bipolar theorem stochastic processes positive supermartingales duality mathematical finance 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Gordan Žitković
    • 1
  1. 1.Department of StatisticsColumbia UniversityNew York

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