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...

We explore the concept of weighted distributions and their role in various phenomena occurring in insurance and finance. In particular, we relate weighted distributions to actuarial and economic premium calculation principles, and also to the capital asset pricing model (CAPM). Imitating the...

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...

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...

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...