no code implementations • 27 Apr 2024 • Fabio Bellini, Tiantian Mao, Ruodu Wang, Qinyu Wu
We introduce a novel axiom of co-loss aversion for a preference relation over the space of acts, represented by measurable functions on a suitable measurable space.
no code implementations • 10 Mar 2024 • Mücahit Aygün, Fabio Bellini, Roger J. A. Laeven
We introduce a notion of GG-convex conjugate, parallel to the classical notion of convex conjugate introduced by Fenchel, and we discuss its properties.
no code implementations • 25 Feb 2023 • Mücahit Aygün, Fabio Bellini, Roger J. A. Laeven
Finally, we provide a general family of strictly consistent scoring functions for Orlicz premia, a myriad of specific examples and a mixture representation suitable for constructing Murphy diagrams.
no code implementations • 6 Sep 2021 • Fabio Bellini, Ilaria Peri
Further, we present a systematic treatment of the properties of $\Lambda$-quantiles, refining some of the results of Frittelli et al. (2014) and Burzoni et al. (2017) and showing that in the case of a nonincreasing $\Lambda$ the properties of $\Lambda$-quantiles closely resemble those of the usual quantiles.
no code implementations • 9 Dec 2020 • Fabio Bellini, Tolulope Fadina, Ruodu Wang, Yunran Wei
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are explored in detail and compared with the widely known and applied inter-quantile differences.
no code implementations • 9 Sep 2020 • Fabio Bellini, Pablo Koch-Medina, Cosimo Munari, Gregor Svindland
We discuss when law-invariant convex functionals "collapse to the mean".
no code implementations • 2 Aug 2018 • Fabio Bellini, Pablo Koch-Medina, Cosimo Munari, Gregor Svindland
We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals.