Bipolar behavior of submodular, law-invariant capacities

Massimiliano Amarante

Statistics & Risk Modeling, 2021, vol. 38, issue 3-4, 65-70

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.

Keywords: Submodular capacities; law-invariant capacities; anticore; Lyapunov theorem; unambiguous events; expected shortfall (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/strm-2020-0025

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