Gini-Type Measures of Risk and Variability: Gini Shortfall, Capital Allocations, and Heavy-Tailed Risks

32 Pages Posted: 11 Sep 2016

See all articles by Edward Furman

Edward Furman

York University - Department of Mathematics and Statistics

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Ricardas Zitikis

University of Western Ontario

Date Written: September 7, 2016

Abstract

We introduce and explore Gini-type measures of risk and variability, and develop the corresponding economic capital allocation rules. The new measures are coherent, additive for co-monotonic risks, convenient computationally, and require only finiteness of the mean. To elucidate our theoretical considerations, we derive closed-form expressions for several parametric families of distributions that are of interest in insurance and finance, and further apply our findings to a risk portfolio of a bancassurance company.

Keywords: risk measure, variability measure, Gini shortfall, Gini capital allocation, Choquet integral.

JEL Classification: C6, G10

Suggested Citation

Furman, Edward and Wang, Ruodu and Zitikis, Ricardas, Gini-Type Measures of Risk and Variability: Gini Shortfall, Capital Allocations, and Heavy-Tailed Risks (September 7, 2016). Available at SSRN: https://ssrn.com/abstract=2836281 or http://dx.doi.org/10.2139/ssrn.2836281

Edward Furman

York University - Department of Mathematics and Statistics ( email )

4700 Keele Street
Toronto, M3J 1P3
Canada

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Ricardas Zitikis

University of Western Ontario ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

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