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From Concentration Profiles to Concentration Maps. New tools for the study of loss distributions

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  • Fontanari, Andrea
  • Cirillo, Pasquale
  • Oosterlee, Cornelis W.

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.

Suggested Citation

  • Fontanari, Andrea & Cirillo, Pasquale & Oosterlee, Cornelis W., 2018. "From Concentration Profiles to Concentration Maps. New tools for the study of loss distributions," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 13-29.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:13-29
    DOI: 10.1016/j.insmatheco.2017.11.003
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    Cited by:

    1. Fontanari, Andrea & Taleb, Nassim Nicholas & Cirillo, Pasquale, 2018. "Gini estimation under infinite variance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 256-269.
    2. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    3. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2021. "Extremal points of Lorenz curves and applications to inequality analysis," Papers 2103.03286, arXiv.org.
    4. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.

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    More about this item

    Keywords

    Concentration measures; Value-at-Risk; Expected Shortfall; Concentration Profile; Gini index;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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