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

Probabilistic predictions can be evaluated through comparisons with observed label
frequencies, that is, through the lens of calibration. Recent scholarship on algorithmic …

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 …

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 …

We discuss when law-invariant convex functionals “collapse to the mean”. More precisely,
we show that, in a large class of spaces of random variables and under mild semicontinuity …

We consider the problem of finding (Pareto-) optimal allocations of risk among finitely many
agents. The associated individual risk measures are law-invariant, but with respect to agent …

In the paper we investigate automatic Fatou property of law-invariant risk measures on a
rearrangement-invariant function space X other than L∞. The main result is the following …

A functional defined on random variables f is law invariant with respect to a reference
probability if its value only depends on the distribution of its argument f under that measure …

Risk and utility functionals are fundamental building blocks in economics and finance. In this
paper we investigate under which conditions a risk or utility functional is sensitive to the …

Short Communication: Revisiting the Automatic Fatou Property of Law-Invariant Functionals |
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