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...

The probabilistic behavior of the claim severity variable plays a fundamental role in calculation of deductibles, layers, loss elimination ratios, effects of inflation, and other quantities arising in insurance. Among several alternatives for modeling severity, the parametric approach continues...

Over the last decade, researchers, practitioners, and regulators had intense debates about how to treat the data collection threshold in operational risk modeling. For fitting the loss severity distribution, several approaches have been employed: the empirical approach, the “naive” approach,...

Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as...

A nonparametric test based on nested L-statistics and designed to compare the riskiness of portfolios was introduced by Brazauskas, Jones, Puri, and Zitikis (2007). Its asymptotic and small-sample properties were primarily explored for independent portfolios, though independence is not a...

Over the last decade, researchers, practitioners, and regulators had intense debates about how to treat the data collection threshold in operational risk modeling. There are several approaches under consideration --- the empirical approach, the "naive'' approach, the shifted approach, and the...

Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as...