Matthias Troffaes, Robert Hable

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Robustness of Natural Extension

Abstract

How sensitive is the natural extension of an upper prevision against small perturbations in the assessments? We revise some basic results from the theory of systems of linear inequalities and equalities, and linear programming, and apply them to the theory of upper previsions. We find that stability is most easily characterized through a regularity condition on the constraints of the primal problem. We then study stability, and the existence of stable representations, in detail. We find necessary and sufficient conditions for the usual representations of natural extension to be stable, and necessary and sufficient conditions for natural extension to have a stable representation at all. We show that, by arbitrary small perturbation, we can force stability of the usual representations.

Keywords

lower prevision, linear programming, robustness, regularity, natural extension, sensitivity, perturbation

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Authors’ addresses

Matthias Troffaes
Department of Mathematical Sciences
Durham University
Science Laboratories, South Road
Durham, DH1 3LE

Robert Hable
Department of Mathematics
University of Bayreuth
D-95440 Bayreuth
Germany

E-mail addresses

Matthias Troffaes		matthias.troffaes@gmail.com
Robert Hable		Robert.Hable@uni-bayreuth.de