Bipolar Theorems for Sets of Non-negative Random Variables

Johannes Langner; Gregor Svindland

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arXiv · 2212.14259

Bipolar Theorems for Sets of Non-negative Random Variables

Johannes Langner·Gregor Svindland

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Abstract

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 non-negative random variables, without any further conditions on the underlying measure space. This generalizes and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modeling.

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BibTeX RIS

Johannes Langner, Gregor Svindland. 2022-12-29. Bipolar Theorems for Sets of Non-negative Random Variables. https://arxiv.org/abs/2212.14259

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