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Bipolar behavior of submodular, law-invariant capacities

Author

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  • Amarante Massimiliano

    (Sciences Économiques, Université de Montréal, Montreal, Quebec H3T 1J4, Canada)

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.

Suggested Citation

  • Amarante Massimiliano, 2021. "Bipolar behavior of submodular, law-invariant capacities," Statistics & Risk Modeling, De Gruyter, vol. 38(3-4), pages 65-70, July.
    • Handle: RePEc:bpj:strimo:v:38:y:2021:i:3-4:p:65-70:n:3
    DOI: 10.1515/strm-2020-0025
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    Cited by:

    1. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, June.

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