Uniqueness of Convex-Ranged Probabilities and Applications to Risk Measures and Games

Massimiliano Amarante, Felix-Benedikt Liebrich () and Cosimo Munari ()
Additional contact information
Felix-Benedikt Liebrich: Amsterdam School of Economics, University of Amsterdam, 1011 NJ Amsterdam, Netherlands
Cosimo Munari: Department of Economics, University of Verona, 37129 Verona, Italy

Mathematics of Operations Research, 2025, vol. 50, issue 1, 743-763

Abstract: We revisit Marinacci’s uniqueness theorem for convex-ranged probabilities and its applications. Our approach does away with both the countable additivity and the positivity of the charges involved. In the process, we uncover several new equivalent conditions, which lead to a novel set of applications. These include extensions of the classic Fréchet–Hoeffding bounds as well as of the automatic Fatou property of law-invariant functionals. We also generalize existing results of the “collapse to the mean”-type concerning capacities and α -MEU preferences.

Keywords: Primary: 91B06; secondary: 91G70; 91A99; 60A99; convex-ranged probabilities; risk measures; games; uniqueness theorem (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2023.0015 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:1:p:743-763

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().