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...

Assuming the multiplicative background risk model, which has been a popular model due to its practical applicability and technical tractability, we develop a general framework for analyzing portfolio performance based on its subportfolios. Since the performance of subportfolios is easier to...

Gini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations, naturally, the classical Pearson correlation coefficient...

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a number of risk measures that are of the form of ratios,...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive...

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...

Determining aggregate risk capital has become a fundamental problem in modern Enterprise Risk Management, and the determination process has been fairly well studied. The consequent exercise of allocating the aggregate risk capital to constituents has also been given high priority in, e.g., both...

In the recent Basel Accords, the Expected Shortfall (ES) replaces the Value-at-Risk (VaR) as the standard risk measure for market risk in the banking sector, making it the most popular risk measure in financial regulation. Although ES is - in addition to many other nice properties - a coherent...