Various methods of combining individual p-values into one p-value are widely used in many areas of statistical applications. We say that a combining method is valid for arbitrary dependence (VAD) if it does not require any assumption on the dependence structure of the p-values, whereas it is...

In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics and optimization. We put a special focus on the class of probability distortions, which is a fundamental tool...

We analyze the question of whether the inf-convolution of law-invariant risk functionals (preferences) is still law-invariant. In economic terms, this question means if all agents in a risk sharing system only care about the distributions of risks, whether the resulting (after risk...