Affiliation:
1. Sciences Économiques , Université de Montréal , Montreal , Quebec H3T 1J4 , Canada
Abstract
Abstract
In the case of a submodular, law-invariant capacity, we provide an entirely
elementary proof of a result of Marinacci
[M. Marinacci,
Upper probabilities and additivity,
Sankhyā Ser. A 61 1999, no. 3, 358–361].
As a corollary, we also show that the anticore of a continuous submodular, law-invariant
nonatomic capacity has a dichotomous nature: either it is one-dimensional or
it is infinite-dimensional. The results have implications for the use of
such capacities in financial and economic applications.
Subject
Statistics, Probability and Uncertainty,Modeling and Simulation,Statistics and Probability
Cited by
2 articles.
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