Enrique Miranda, Marco Zaffalon

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Computing the conglomerable natural extension

Abstract

Given a coherent lower prevision P, we consider the problem of computing the smallest coherent lower prevision C greater than P that is conglomerable, in case it exists. C is called the conglomerable natural extension. Past work has shown that C can be approximated by an increasing sequence of coherent lower previsions. We close an open problem by showing that this sequence can be infinite, while being made of distinct elements. Moreover, we give sufficient conditions, of quite broad applicability, to make sure that the point-wise limit of the sequence is C in case P is the lower envelope of finitely many linear previsions. In addition, we study the question of the existence of C and its relationship with the notion of marginal extension.

Keywords

coherent lower previsions, conglomerability, conglomerable natural extension, natural extension, marginal extension

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E-mail addresses

Enrique Miranda		mirandaenrique@uniovi.es
Marco Zaffalon		zaffalon@idsia.fr