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Positivity

pp 1–19 | Cite as

Fatou closedness under model uncertainty

  • Marco Maggis
  • Thilo Meyer-Brandis
  • Gregor Svindland
Article
  • 30 Downloads

Abstract

We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of \({\mathcal P}\)-quasisure bounded random variables, where \({\mathcal P}\) is a (possibly non-dominated) class of probability measures. Applications of our results lie within robust versions the Fundamental Theorem of Asset Pricing or dual representation of convex risk measures.

Keywords

Capacities Fatou closedness/property Sequential order closedness Convex duality under model uncertainty Fundamental Theorem of Asset Pricing 

Mathematics Subject Classification

31A15 46A20 46E30 60A99 91B30 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Marco Maggis
    • 1
  • Thilo Meyer-Brandis
    • 2
  • Gregor Svindland
    • 2
  1. 1.Department of MathematicsUniversity of MilanMilanItaly
  2. 2.Mathematics InstituteLMU MunichMunichGermany

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