A Nonlinear Sandwich Theorem

Mario Ghossoub (), Giulio Principi () and Lorenzo Stanca ()
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Mario Ghossoub: Department of Statistics and Actuarial Science, University of Waterloo, Canada;
Giulio Principi: Department of Economics, New York University, USA;
Lorenzo Stanca: Department of Economics, Social Studies, Applied Mathematics and Statistics (ESOMAS) and Collegio Carlo Alberto, University of Torino, Italy;

No 81, Working papers from Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino

Abstract: We provide a Sandwich Theorem (Konig (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.

Keywords: Sandwich Theorem; Pataraia's Theorem; C-(super/sub)linearity; convex-conic symmetric preorder. (search for similar items in EconPapers)
JEL-codes: C00 C02 C65 C69 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2023-04
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