Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure

Serena Doria ()

Annals of Operations Research, 2012, vol. 195, issue 1, 33-48

Abstract: A model of coherent upper conditional prevision for bounded random variables is proposed in a metric space. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff dimension, it is defined by a 0–1 valued finitely, but not countably, additive probability. If the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension it is proven that a coherent upper conditional prevision is uniquely represented by the Choquet integral with respect to the upper conditional probability defined by Hausdorff outer measure if and only if it is monotone, comonotonically additive, submodular and continuous from below. Copyright Springer Science+Business Media, LLC 2012

Keywords: Coherent upper conditional prevision; Hausdorff outer measure; Choquet integral; Comonotonic additivity; Submodularity; Continuity from below (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10479-011-0899-y

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