This is an announcement for the paper "A filtered version of the bipolar theorem of Brannath and Schachermayer" by Gordan Zitkovic.
Abstract: We extend the Bipolar Theorem of Brannath and Schachermayer (1999) to the space of nonnegative cadlag 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 (1999) and give a budget-constraint characterization of admissible consumption processes in an incomplete semimartingale market.
Archive classification: math.PR math.FA
Citation: Journal of Theoretical Probability (2005) vol. 15 no. 1
The source file(s), Bipolar.tex: 58142 bytes, is(are) stored in gzipped form as 0706.0049.gz with size 18kb. The corresponding postcript file has gzipped size 101kb.
Submitted from: gordanz@math.utexas.edu
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