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<p>This paper assumes a robust, in general not dominated probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of nonnegative random variables without any further conditions on the underlying measure space. This generalises and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modelling.</p>

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Bipolar theorems for sets of nonnegative random variables

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • Johannes Langner,
  • Gregor Svindland

摘要

This paper assumes a robust, in general not dominated probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of nonnegative random variables without any further conditions on the underlying measure space. This generalises and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modelling.