From Concentration Profiles to Concentration Maps. New Tools for the Study of Loss Distributions.

34 Pages Posted: 13 Oct 2016 Last revised: 1 Dec 2017

See all articles by Andrea Fontanari

Andrea Fontanari

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM)

Pasquale Cirillo

Delft University of Technology; Delft University of Technology - Delft Institute of Applied Mathematics (DIAM)

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: June 8, 2017

Abstract

We introduce a novel approach to risk management, based on the study of concentration measures of the loss distribution. We show that indices like the Gini index, especially when restricted to the tails by conditioning and truncation, give us an accurate way of assessing the variability of the larger losses – the most relevant ones – and the reliability of common risk management measures like the Expected Shortfall. We first present the Concentration Profile, which is formed by a sequence of truncated Gini indices, to characterize the loss distribution, providing interesting information about tail risk. By combining Concentration Profiles and standard results from utility theory, we develop the Concentration Map, which can be used to assess the risk attached to potential losses on the basis of the risk profile of a user, her beliefs and historical data. Finally, with a sequence of truncated Gini indices as weights for the Expected Shortfall, we define the Concentration Adjusted Expected Shortfall, a measure able to capture additional features of tail risk. Empirical examples and codes for the computation of all the tools are provided.

Keywords: concentration profile, concentration map, Gini index, Lorenz curve, CAES, ES, VaR

JEL Classification: C43, C46, G32

Suggested Citation

Fontanari, Andrea and Cirillo, Pasquale and Oosterlee, Cornelis W., From Concentration Profiles to Concentration Maps. New Tools for the Study of Loss Distributions. (June 8, 2017). Available at SSRN: https://ssrn.com/abstract=2850949 or http://dx.doi.org/10.2139/ssrn.2850949

Andrea Fontanari (Contact Author)

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM) ( email )

Mekelweg 4
Delft, Holland 2628
Netherlands

Pasquale Cirillo

Delft University of Technology ( email )

Stevinweg 1
Stevinweg 1
Delft, 2628 CN
Netherlands

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM) ( email )

Mekelweg 4
Delft, Holland 2628
Netherlands

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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