A Nonlinear Sandwich Theorem

Mario Ghossoub; Giulio Principi; Lorenzo Stanca

doi:10.48550/arxiv.2304.02818

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A Nonlinear Sandwich Theorem

Mario Ghossoub, Giulio Principi and Lorenzo Stanca

ArXiv.org

arXiv

04/05/2023

DOI: 10.48550/arxiv.2304.02818

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We provide a Sandwich Theorem (König (1972)) for positively homogeneous functionals that satisfy additivity only on a restricted domain. Our relaxation of additivity is based on a binary relation called convex-conic symmetric preorder, whereby additivity is restricted to all couples of elements that belong to such relation. We then study applications of our nonlinear Sandwich Theorem, proving extension and envelope representation results. Finally, we consider some applications to comonotonicity, a key property in decision theory, risk measurement, and the theory of risk sharing.

Mathematics - Functional Analysis

Details

Title: Subtitle: A Nonlinear Sandwich Theorem
Creators: Mario Ghossoub
Giulio Principi
Lorenzo Stanca
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2304.02818
ISSN: 2331-8422
Publisher: arXiv
Language: English
Date posted: 04/05/2023
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9985179964302771

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