We consider distributional free inference to test for positive quadrant dependence, i.e. for the probability that two variables are simultaneously small (or large) being at least as great as it would be were they dependent. Tests for its generalisation in higher dimensions, namely positive...

We propose inference tools to analyse the ordering of concordance of random vectors. The analysis in the bivariate case relies on tests for upper and lower quadrant dominance of the true distribution by a parametric or semiparametric model, i.e. for a parametric or semiparametric model to give a...

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics...

We consider distributional free inference to test for positive quadrant dependence, that is, for the probability that two variables are simultaneously small (or large) being at least as great as it would be were they dependent. Tests for its generalization to higher dimensions, namely positive...

Actuaries intuitively feel that positive correlations between individual risks reveal a more dangerous situation compared to independence. The purpose of this short note is to formalize this natural idea. Specifically, it is shown that the sum of risks exhibiting a weak form of dependence known...

We demonstrate both analytically and numerically that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This...

The problems of detecting, classifying, and estimating shapes in point cloud data are important due to their general applicability in image analysis, computer vision, and graphics. They are challenging because the data is typically noisy, cluttered, and unordered. We study these problems using a...

A prominent problem in actuarial science is to define, or describe, premium calculation principles (pcp's) that satisfy certain properties. A frequently used resolution of the problem is achieved via distorting (e.g., lifting) the decumulative distribution function, and then calculating the...

By extending the notion of weighted premium calculation principles, we introduce weighted risk capital allocations, explore their properties, and develop computational methods. When achieving these goals, we find it particularly fruitful to relate the weighted allocations to general Stein-type...