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Bipolar Theorems for Sets of Non-negative Random Variables

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  • Johannes Langner
  • Gregor Svindland

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 generalises and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modeling which we discuss throughout the paper.

Suggested Citation

  • Johannes Langner & Gregor Svindland, 2022. "Bipolar Theorems for Sets of Non-negative Random Variables," Papers 2212.14259, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2212.14259
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    References listed on IDEAS

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    1. Niushan Gao & Cosimo Munari, 2020. "Surplus-Invariant Risk Measures," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1342-1370, November.
    2. Matteo Burzoni & Marco Maggis, 2019. "Arbitrage-free modeling under Knightian Uncertainty," Papers 1909.04602, arXiv.org, revised Apr 2020.
    3. Felix-Benedikt Liebrich & Marco Maggis & Gregor Svindland, 2020. "Model Uncertainty: A Reverse Approach," Papers 2004.06636, arXiv.org, revised Mar 2022.
    4. Marco Maggis & Thilo Meyer-Brandis & Gregor Svindland, 2016. "The Fatou Closedness under Model Uncertainty," Papers 1610.04085, arXiv.org, revised Oct 2018.
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