Sub-Additive Aggregation Functions and Their Applications in Construction of Coherent Upper Previsions

Serena Doria, Radko Mesiar and Adam Šeliga
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Serena Doria: Department of Engineering and Geology, University G. d’Annunzio, 66100 Chieti-Pescara, Italy
Radko Mesiar: Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia
Adam Šeliga: Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia

Mathematics, 2020, vol. 9, issue 1, 1-12

Abstract: In this paper, we explore the use of aggregation functions in the construction of coherent upper previsions. Sub-additivity is one of the defining properties of a coherent upper prevision defined on a linear space of random variables and thus we introduce a new sub-additive transformation of aggregation functions, called a revenue transformation, whose output is a sub-additive aggregation function bounded below by the transformed aggregation function, if it exists. Method of constructing coherent upper previsions by means of shift-invariant, positively homogeneous and sub-additive aggregation functions is given and a full characterization of shift-invariant, positively homogeneous and idempotent aggregation functions on [ 0 , ∞ [ n is presented. Lastly, some concluding remarks are added.

Keywords: sub-additivity; revenue transformation; aggregation function; coherent upper prevision (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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