TY - JOUR
T1 - Stochastic ordering of Gini indexes for multivariate elliptical risks
AU - Kim, Bara
AU - Kim, Jeongsim
N1 - Funding Information:
We are grateful to the reviewer for valuable comments and suggestions, which greatly improved this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1A2B4012676 ). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2017R1D1A1B03029542 ).
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/9
Y1 - 2019/9
N2 - In this paper, we show that the conjecture, made by Samanthi et al. (2016), on the ordering of Gini indexes of multivariate normal risks with respect to the strength of dependence, is not true. By using the positive semi-definite ordering of covariance matrices, we can obtain the usual stochastic order of the Gini indexes for multivariate normal risks. This can be generalized to multivariate elliptical risks. We also investigate the monotonicity of the Gini indexes in the usual stochastic order when the covariance (dispersion, resp.) matrices of multivariate normal (elliptical, resp) risks increase componentwise. In addition, we derive a large deviation result for the Gini indexes of multivariate normal risks.
AB - In this paper, we show that the conjecture, made by Samanthi et al. (2016), on the ordering of Gini indexes of multivariate normal risks with respect to the strength of dependence, is not true. By using the positive semi-definite ordering of covariance matrices, we can obtain the usual stochastic order of the Gini indexes for multivariate normal risks. This can be generalized to multivariate elliptical risks. We also investigate the monotonicity of the Gini indexes in the usual stochastic order when the covariance (dispersion, resp.) matrices of multivariate normal (elliptical, resp) risks increase componentwise. In addition, we derive a large deviation result for the Gini indexes of multivariate normal risks.
KW - Elliptical distribution
KW - Gini index
KW - Large deviation
KW - Positive semi-definite
KW - Usual stochastic order
UR - http://www.scopus.com/inward/record.url?scp=85068999081&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2019.07.002
DO - 10.1016/j.insmatheco.2019.07.002
M3 - Article
AN - SCOPUS:85068999081
SN - 0167-6687
VL - 88
SP - 151
EP - 158
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -