A Filtered Version of the Bipolar Theorem of Brannath and Schachermayer

Gordan Žitković ()
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Gordan Žitković: Columbia University

Journal of Theoretical Probability, 2002, vol. 15, issue 1, 41-61

Abstract: 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.

Keywords: bipolar theorem; stochastic processes; positive supermartingales; duality; mathematical finance (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013885121598

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