Capital Allocation for Set-Valued Risk Measures

Electronic version of an article published as [International Journal of Theoretical and Applied Finance, Volume 23, Number 1, 2020, 16 pages] [DOI/10.1142/S0219024920500090] © [copyright World Scientific Publishing Company]

Posted: 1 Feb 2021

See all articles by Francesca Centrone

Francesca Centrone

Università del Piemonte Orientale - Dipartimento di Studi per l'Economia e l'Impresa

Emanuela Rosazza Gianin

University of Milano-Bicocca - Dip. di Statistica e Metodi Quantitativi

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Date Written: February 27, 2020

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.

Keywords: Risk management, capital allocation rules, set-valued risk measures, coherent and convex risk measures

JEL Classification: G32

Suggested Citation

Centrone, Francesca and Rosazza Gianin, Emanuela, Capital Allocation for Set-Valued Risk Measures (February 27, 2020). Electronic version of an article published as [International Journal of Theoretical and Applied Finance, Volume 23, Number 1, 2020, 16 pages] [DOI/10.1142/S0219024920500090] © [copyright World Scientific Publishing Company] , Available at SSRN: https://ssrn.com/abstract=3663017

Francesca Centrone

Università del Piemonte Orientale - Dipartimento di Studi per l'Economia e l'Impresa ( email )

Via Perrone 18
Novara, 28100
Italy

Emanuela Rosazza Gianin (Contact Author)

University of Milano-Bicocca - Dip. di Statistica e Metodi Quantitativi ( email )

Milan
Italy

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