``The rich are getting richer'' implies that the population income distributions are getting more right skewed and heavily tailed. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are all...

To accommodate numerous practical scenarios, in this paper we extend statistical inference for smoothed quantile estimators from finite domains to infinite domains. We accomplish the task with the help of a newly designed truncation methodology for discrete loss distributions with infinite...

We derive consistency, asymptotic normality, and standard error estimation for the tail conditional allocation, also known as the marginal expected shortfall, under minimal conditions and thus geared toward widest applicability. These advances have become possible due to a newly developed...

In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this paper, we introduce, justify, and explore several new...

To assess the required capital for insurance companies, which usually have several business lines, estimates of the joint tail probabilities of aggregate losses are needed. Under the collective risk model, these aggregate losses are sums of random number of random variables, whose distributions...

The prominence of the Euler allocation rule (EAR) is rooted in the fact that it is the only return on risk-adjusted capital (RORAC) compatible capital allocation rule. When the total regulatory capital is set using the value-at-risk (VaR), the EAR becomes -- using a statistical term -- the...

Financial institutions manage operational risk by carrying out the activities required by regulation, such as collecting loss data, calculating capital requirements, and reporting. The information necessary for this purpose is then collected in the OpRisk databases. Recorded for each OpRisk...

The tail conditional allocation plays an important role in a number of areas, including economics, finance, insurance, and management. Fixed-margin confidence intervals are of particular interest, and the assessment of their coverage probabilities is of much interest in practice. In this paper...

When developing large-sample statistical inference for quantiles, also known as Values-at-Risk in finance and insurance, the usual approach is to convert the task into sums of random variables. The conversion procedure requires that the underlying cumulative distribution function (cdf) would...