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Capital Allocation For Set-Valued Risk Measures

Author

Listed:
  • FRANCESCA CENTRONE

    (Dipartimento di Studi per l’Economia e l’Impresa, Università del Piemonte Orientale, Via Perrone 18, 28100 Novara, Italy)

  • EMANUELA ROSAZZA GIANIN

    (Dipartimento di Statistica e Metodi Quantitativi, Università di Milano Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy)

Abstract

We introduce the definition of set-valued capital allocation rule, in the context of set-valued risk measures. In analogy to some well known methods for the scalar case based on the idea of marginal contribution and hence on the notion of gradient and sub-gradient of a risk measure, and under some reasonable assumptions, we define some set-valued capital allocation rules relying on the representation theorems for coherent and convex set-valued risk measures and investigate their link with the notion of sub-differential for set-valued functions. We also introduce and study the set-valued analogous of some properties of classical capital allocation rules, such as the one of no undercut. Furthermore, we compare these rules with some of those mostly used for univariate (single-valued) risk measures. Examples and comparisons with the scalar case are provided at the end.

Suggested Citation

  • Francesca Centrone & Emanuela Rosazza Gianin, 2020. "Capital Allocation For Set-Valued Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-16, February.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:01:n:s0219024920500090
    DOI: 10.1142/S0219024920500090
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    References listed on IDEAS

    as
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