Bipolar Theorems for Sets of Non-negative Random Variables
Probability
2026-05-21 v5 Functional Analysis
Mathematical Finance
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.
Cite
@article{arxiv.2212.14259,
title = {Bipolar Theorems for Sets of Non-negative Random Variables},
author = {Johannes Langner and Gregor Svindland},
journal= {arXiv preprint arXiv:2212.14259},
year = {2026}
}