Ordering Gini Indexes of Multivariate Elliptical Risks

22 Pages Posted: 13 Apr 2016 Last revised: 11 Apr 2019

See all articles by Ranadeera Samanthi

Ranadeera Samanthi

Central Michigan University

Wei Wei

University of Wisconsin - Milwaukee

Vytaras Brazauskas

University of Wisconsin - Milwaukee

Date Written: April 12, 2016

Abstract

In this paper, we establish several stochastic orders between Gini indexes of multivariate elliptical risks with the same marginals but different dependence structures. This work is motivated by the studies of Brazauskas et al (2007) and Samanthi et al (2015), who employed the Gini index to compare the riskiness of insurance portfolios. Using Monto Carlo simulations, they found that that the power function and probability of type I error of the associated hypothesis test increase as portfolios become more positively correlated. The comparison of Gini indexes presented in this paper provides a theoretical explanation to this statistical phenomenon. Moreover, it enriches the studies of the problem of central concentration of multivariate elliptical distributions and generalizes the pd-1 order proposed by Shaked and Tong (1985).

Keywords: Gini index, elliptical distribution, dependence structure, comonotonicity, usual stochastic order, increasing convex order, supermodular order, pd-1 order

Suggested Citation

Samanthi, Ranadeera and Wei, Wei and Brazauskas, Vytaras, Ordering Gini Indexes of Multivariate Elliptical Risks (April 12, 2016). Insurance: Mathematics and Economics, 68(3), 84-91, 2016, Available at SSRN: https://ssrn.com/abstract=2675886

Ranadeera Samanthi

Central Michigan University ( email )

Department of Mathematics
Pearce Hall 206I
Mt Pleasant, MI 48859
United States

Wei Wei (Contact Author)

University of Wisconsin - Milwaukee ( email )

Bolton Hall 802
3210 N. Maryland Ave.
Milwaukee, WI 53211
United States

Vytaras Brazauskas

University of Wisconsin - Milwaukee ( email )

Bolton Hall 802
3210 N. Maryland Ave.
Milwaukee, WI 53201
United States

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