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 …

In this paper, monetary risk measures that are positively superhomogeneous, called star-
shaped risk measures, are characterized and their properties are studied. The measures in …

This paper presents novel characterization results for classes of law-invariant star-shaped
functionals. We begin by establishing characterizations for positively homogeneous and star …

The notion of “tail risk” has been a crucial consideration in modern risk management and
financial regulation, as very well documented in the recent regulatory documents. To …

Entropy is a measure of self information or uncertainty. Using different concepts of entropy,
we may get different risk measures by dual representation. In this paper, we introduce and …

We introduce and study the main properties of a class of convex risk measures that refine
Expected Shortfall by simultaneously controlling the expected losses associated with …

Motivated by recent advances on elicitability of risk measures and practical considerations of
risk optimization, we introduce the notions of Bayes pairs and Bayes risk measures. Bayes …

We establish general “collapse to the mean” principles that provide conditions under which
a law-invariant functional reduces to an expectation. In the convex setting, we retrieve and …

Inspired by the recent developments in risk sharing problems for the value at risk (VaR), the
expected shortfall (ES), and the range value at risk (RVaR), we study the optimization of risk …

We systematically study pairwise counter-monotonicity, an extremal notion of negative
dependence. A stochastic representation and an invariance property are established for this …